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UNITED STATES OF AMERICA. 






ELEMENTS 

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ASTRONOMY 






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ELEMENTS 



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WITH METHODS FOR DETERMINING THE 

LONGITUDES, ASPECTS, Sec. OFTHE PLANETS 

TOR ANY FUTURE TIME ; 

AND AN 

EXTENSIVE SET OF GEOGRAPHICAL AND ASTRONOMI- 
CAL PROBLEMS ON THE GLOBES. 

DESIGNED FOR THE 

USB OF SCHOOLS AND JUNIOR STUDENTS, 



By S. TREEBY, 

TEACHER OF THE MATHEMATICS, CLASSICS, &C. &€„ 



REVISED AND CORRECTED ~ 
V 

Br M. NASH, 

TEACHER OF MATHEMATICS, NEW-YORK: 

NEW- YORK: 

PUBLISHED BY SAMUEL WOOD & SONS> 
NO. 261, PEARL-STREET ; 

Aad Samuel S. Wood & Co. No. 212, Market-street , 
Baltimore. 

1823. 



SOUTHERN DISTRICT OP NEW-YORK, ss. 

fjJ!TREMEMBERED,That|on the twenty-eighth day of March, 
} _~^™-j ^ t jje forty-seventh year of the Independence of the 
$ ij- ss. } United States of America, Samuel Wood & Sons, of the 
f-^0,^0.5 said District, have deposited in this office, the title of 
a book the right whereof they claim as proprietors, in the words 
following, to • ><: • 

" The Elements, of Astronomy ; with methods for determining the 
longitudes, aspects, &c. of the planets for any future time; and an 
extensive set of Geographical and Astronomical Problems on the 
Globes. Designed for the use of schools and junior students. By 
fe. Treeby, teacher of the Mathematics, Classics, &c. &c Revised 
and corrected byM. Nash, teacher of Mathematics, New-York." 

£n conformity to the Act of Congress of the tniteu > fates* 
entitled, " An act for the encouragement of learning, by securing the 
copies of Maps, Charts, and Books, to the Authors and Proprietor* 
of such copies, during the time therein mentioned :" and also 
loan Act, entitled, "An Act, supplementary to an Aet, entitled 
an Act for thr -ncouragement of learning, by securing the 
copies of Map? Charts, and Books, to the A uthors and Propri- 
etors of such copies during the times therein mentioned, and ex- 
tending the benefits thereof fc the arts of designing- engraving, 
and etching historic* anrf other prints ' 
JAMES DILL, 

Clerk of the Southern District of New-York, 



2/£ 



y 



ADTERTISEMENT 



A judicious compendium of the science of As- 
tronomy, and at the same time a suitable one for 
rendering a knowledge of it accessible to young 
persons, has long been wanted in our schools, and 
sought for in vain. Treeby^s Elements is em- 
inently calculated to supply this deficiency. The 
arrangement of the work, the perspicuity of the 
style, and the elegant plates, peculiarly adapt it 
to the capacities of youth, or those who wish to 
acquire a general knowledge of the science by 
private study. 

I would recommend to teachers, when exercis- 
ing their pupils in planetary problems by the 
globes, to ascertain the latitudes and longitudes 
of the planets from a Nautical Almauac, or from 
the Diary or United States Almanac, and mark 
their positions on the Globe, as directed in a note 
to Problem XXVI J I. page 145. 

M. NASH, 

New-York, 28th March, 1823. 



J* 



PREFACE. 



Of all the subjects that engage the lucubrations of the 
sage, the speculations of the philosopher, or which en- 
rich the understandings of mankind, Astronomy is, 
without competition, the most sublime. It is nothing 
less than the contemplation of the operations of omnipo- 
tent power, directed by infinite wisdom, which are cir- 
culated through boundless space, for the happiness of an 
Incalculable number of created beings, whether they 
live with us upon the earth, are inhabitants of our sat- 
ellite the Moon, or residents of the purer regions of 
Mercury, or the denser climates of Saturn ; all are the 
offspring of one benign parent, and partake alike of his 
fatherly munificence. 

The science of Astronomy is not speculative, but its 
truths are demonstrable as its study is sublime. Pro- 
ceeding upon principles, which are incontestable, the 
Astronomer informs us of the velocity of any celestial 
body ,however swift its motion; its magnitudes,however 
extensive ; its distance, however remote ; he traces its 
orbit, whatever fye its orbicular curve ; he beautifully 
harmonises the varieties of our seasons ; illustrates $$ 



\t PREFACE. 

causes of our unequal days and nights ; he informs us 
the altitudes of the variegated clouds, which so copious- 
ly emanate from the earth, shows us the swiftness with 
which they skim through our atmosphere ; and, as he is 
acquainted with the various motions of the celestial bo- 
dies, so he predicts their configurations for any future 
period, however distant, with a certainty, which those 
unacquainted with astronomical investigations behold 
with astonishment ; but its utility is as apparent as its 
contemplation is majestic ; by its knowledge commerce 
is promoted, and the intercourse between distant nations 
facilitated, so that the exuberant fertility of one coun- 
try is exported to supply the barrenness of another.and 
With the assistance of its knowledge, the mariner guides* 
his vessel across the trackless ocean, with as much cer- 
tainty as he displays in his pedestrious journey from one 
well known place to another. A farther proof of its 
utility, is, its universal cultivation, combined with the 
characters of its students. It is not only in England or 
France that Astronomy is cultivated, but in Germany, 
in Denmark, nay, in every civilized nation of the world, 
observatories are erected, which oracularly prove, that 
this is considered the pre-eminent of the sciences ; and, 
as genius and talent are elicited by public patronage, so 
the greatest and most learned men, in all ages, have 
l>een dignified by the appellation Astronomers. From 
a consideration of the sublimity and utility of the sci- 
ence, we cannot wonder that treatises thereon are nu- 
merous, or that efforts have been made to reduee Hs 



PBEFACE* VI! 

truths to the level of the juvenile capacity ; and yet, 
probably owing to the profundity of erudition enjoyed 
by the respective writers, there does not exist a single 
isolated volume calculated for the general purposes of 
scholastic education ; and the writer of this is persuad- 
ed, that this sublime science has been secluded from 
many seminaries, teachers not having been able to pro- 
cure an elementary volume suited to the ages and un- 
derstandings of their pupils. The design of the author 
of the present work is to supply this deficiency ; and, as 
plainness, united with a desire to be understood, rather 
than to be admired, have been the objects he has had 
constantly in view ; as he has not endeavoured to dis- 
play his learning by copying or inventing a multiplicity 
of analytical expressions or unnecessary technical 
phrases ; as he intends to use the work in his own school; 
and, as he has had considerable experience in education, 
he imagines he has succeeded It is unnecessary mi- 
nutely to describe the present work,or pursue it through 
its various ramifications j its merits or defects will be 
easily observed from a perusal of its contents ; but it 
must be obvious from inspection, that it not only con* 
tains " multum in parvo," but " multum ad parvunv'? 

The planetary problems are a novelty in an astronom- 
ical work, and have not hitherto been published, that 
the author ha? ever seen : they will furnish the student 



vm tkefacb:. 

who has made some proficiency in arithmetic, witk 
amusement as well as information. 

The problems to be performed by tbe globes, will be 
found particularly adapted to the study of that pleas- 
ing, interesting, and instructive department ofedu^ 
cation ; among them is the manner of solution of the 
problem for determining the time exf shortest twilight, 
being in no other work extant : the solution of this 
problem has caused mathematicians much trouble, and 
lias been the cause of acrimonious altercations among 
them. 

The vocabulary of astronomical terms, &c. &c. at the 
end of the work, is an agreeable and a useful accompan- 
iment ; it will be particularly atlvantageous to thestu* 
dent, by being committed to memory, as his age or ca- 
pacity may determine. The book of questions on this 
treatise, is essentially necessary to the student, who 
wishes to have a complete knowledge of the facts inter- 
spersed through the work, as they are discriminately 
arranged, and bear immediately on the facts, they are ad- 
mirably calculated to imprint the subject on his mind ; 
they are divided into two sections; the first bearing up- 
on the numbered articles, and the second on the observa- 
tions. 

The present, work, with the book of questions, are 
not only well adapted to seminaries in which young 
gentlemen are educated, but in seminaries of female e«(u* 



PREFACE. IX 

Hatiofe they will be found particularly suited ; and young 
ladies may from them be as easily initiated into the ru- 
diments of Astronomy, as they are taught English gram- 
mar, geography, or any branch of female education. 

In conclusion, the author will elucidate the method 
lie adopts in exercising his pupils, to ascertain and facil- 
itate their progress in any particular branch of litera- 
ture, which experience has evinced te be a successful 
plan, and according to which, " The Elements of As- 
tronomy" may be used in any seminary with success, 
He furnishes those of them who are able to read tolera- 
bly well with the treatise, and denominates them " The 
Astronomical Class;" once in a day he calls the said 
class to read ; when they have read three or four pages, 
without the observations, Which they read after having 
gone through the work once, they turn to the question, 
book, and ask themselves three or four rounds of ques* 
tions therefrom ; No. 2 first asks No. 1 ; No. 3 then asks 
No. 2, and so on, taking notice that the last round of 
questions be from the Vocabulary : frequently the writer 
interrogates them more satisfactorily to prove their 
proficiency. Two or three times a week he gives them 
an astronomical exercise, which consists of about 
six questions delivered out prior to their leaving 
school on an evening, which they are required to an- 
swer written at length upon their slates by the ensuing 
morning: this, as well as employing them at home, 
teaches them to spell correctly, write fluently, and learn 
Astronomy simultaneously ; and, upon this plan,Englisfo 



X PREFACE, 

grammar, geography, history, or almost any branch of 
literature may be successfully taught. After having 
said thus much, he has only to notice, that he intends to 
accommodate those teachers whose pupils are numer- 
ous, with a key to the question-book, which will also 
contaiu solutions to the questions on the planetary prob- 
lems in this work as soon as opportunity will allow ; in 
the mean time he casts liis work upon the good sense 
and candour of an enlightened public ; and should it be 
so fortunate as to be considered by them adequate to 
answer its design, he shall consider his labour not uii= 
profitably bestowed. 

Plymouth, January 5, 1821 - 



ELEMENTS 



OE 



ASTRONOMY, 

&c. &c. 



PART L 



ASTRONOMICAL DEFINITIONS. 

.1. A planet is an opaque body, which revolves 
around, derives light from, and shines by the 
help of another body. 

Planets are divided into Primary and Second- 
ary. 

2. A comet is a body which moves round the 
sun, in a very eccentric orbit or tract, and is 
usually accompanied with a shining tail. 

3. The orbit of any celestial body is the curve, 
-or path it describes,iu revolving around another. 
The orbits of the planets are elliptical. 

4. The axis of a celestial body is an imaginary 



ASTRONOMY. 



OF THE DIVISIONS OF THE CELESTIAL 
BODIES, WITH A DESCRIPTION OF " THE 
SOLAR SYSTEM." 

1. Astronomy is that branch of natural phi- 
losophy, which treats of, and describes, the ap- 
pearances, properties, motions, magnitudes, per- 
iods, eclipses, distances, and the various phenom* 
eua of the celestial bodies, 

2. The determination of the magnitudes, dis- 
tances, and the orbits of the celestial bodies, is 
called plane or pure astronomy; and the investi- 
gation of the causes of their motions, is called 
physical astronomy. 

3. Pure astronomy is determined from observ- 
ations on the apparent magnitudes amd motions 
of the heavenly bodies. 

4. Physical astronomy is founded principally 
on analogy, by applying the laws of motion, to 
the observations of the planets and stars. 

5. The celestial bodies are generally divided 
into two sections, viz. the solar system, and the 
universe, 

6. The solar system is composed of a certain 
number of celestial bodies, which revolve around 




-&-3/ziverirfi 



Tmm mm&m, &r&Tmm* 



THE SOLAR SYSTEM. 17 

the sun as a centre : they are divided into plan- 
ets, comets, and asteroids. 

7. The particular situations of these planets, 
comets, aud asteroids, with respect to the sun, is 
the reason why the system is called " The Solar 
System," because they revolve around that lumi- 
nary as a centre. 

Obs. — The curve which each planet respectively de- 
scribes in revolving about the sun, is an ellipse; and the 
sun is in a focus of such elliptic curve. Plate III. Fig. 
1. IfPe g d g' P be any planet's orbit, S is the posi- 
tion of the sun. 

8. The solar system is composed of the Sun> 
marked © in the centre : 

Of seven primary planets, viz. Mercury £, 
Venus 9 , the Earth @, Mars £ , Jupiter % > 
Saturn h , and Herschell # : 

Of four asteroids, or minor planets, named 
Ceres, Pallas, Juno and Vesta : 

Of eighteen secondaiy planets, satellites, or 
moons : the earth has one moon attending it ; Ju- 
piter has four ; Saturn has seven ; and Herschell 
has six: 

And of a considerable number of comets. 

9. The planets are divided into primary and 
secondary ; they are also distinguished by the 
names of Superior and Inferior. 

10. The primary planets are those bodies 
which revolve around the Sun, as a centre : they 
are Mercury, Venus, the Earth, Mars, Jupiter, 
Saturn, and Herschell. Each planet, besides 
this revolution, has a motion on its axis ; and the 
time it is revolving thereon, is the length of its 
day. 

2* 



la 



THE SOLAR SYSTEM. 



11. The secondary planets are those bodies 
which revolve around a primary as a centre : 
they are also called satellites or moons, The of- 
fice of a secondary planet is, to reflect the light 
of the sun to its primary during the night, just as 
the moon reflects the light of the sun to us ; the 
secondary planets have also a motion on their 
axis, by which means they have day and night 
in the same regular succession as we have. 

12, The superior planets are Mars, Jupiter, 
Saturn and Herschell ; they are so called, be- 
cause their orbits are outside the orbit of the 
earth. 

13. The inferior planets are Mercury and 
Venus ; they are so called, because their orbits 
are within the orbit of the earth. 

14. The distances of the planets from the sun, 
their respective diameters in English miles, with 
the times of their various revolutions around the 
sun, in the days of our year, are as follow : — 



" 


Distance 








in 


Diameter 


Period 


Planets, 


millions 
of miles. 


in miles. 


in days. 


Mercury - - 


37 


3,108 


83 


Venus - - - 


69 


7,498 


225 


Earth - - - 


95 


7,964 


365 


Mars - - - 


145 


4,444 


687 


Jupiter - - - 


494 


90,145 


4,332 


Saturn - - ^ 


906 1 77,950 


10,759 


{Herschell - - 


1,813 


1 34,404 


31,346 



OF THE SUN, 



OF THE SUN. 



19 



15. The sun is in the centre of the solar sys- 
tem, and from thence, by his genial rays, causes 
the planets to be fit habitations for created be- 
ings, and by means of his fructifying heat, 
they vegetate, for the animation and support of 
their various inhabitants. 

Obs. — That the sun, moon, and planets are stored with 
inhabitants, we have every reason to believe, because 
they areas well provided with the means of supporting 
animals and inhabitants in general, as the planet on 
which we reskle, has the inherent properties of provid- 
ing sustenance for us ; and there is no doubt, but that 
the all-wise Creator of the Heavens, has varied the con- 
stitutions of his family, so as to suit the respective plan- 
et he intends for them to occupy. 

16. The sun is the only body in the solar sys- 
tem which shines by its own light, it is a large 
globe of 870,000 miles in diameter, and it per- 
forms a revolution on its axis 5 once in twenty -five 
days. 

Obs. — The time the sun takes to revolve on its axis 
is determined, by observing the gradual motion of any 
particular spot on its surface ; these phenomena were 
first observed by Galileo; and, as they revolve around 
the sun, as that body revolves on its axis, so if we no- 
tice how many days a particular spot is moving from one 
edge of the sun to the other opposite, so many days is 
half the time, the sun is revolving on its axis, which be- 
ing doubled, will be the time required. 

17. The sun's apparent diameter is greater in 
winter than it is in summer ; the earth is there- 



20 OF THE SUN. 

fore nearer to the suu at the former, than at the 
latter period. 

Obs. 1. — The sun's apparent diameter is the angle the 
diameter of the sun forms at the surface of the earth. 
This angle in December is $2 r 35", and in June it is on- 
ly 31' Si". The farther any body is from any particular 
place, the less angle it forms; and the nearer it is, the 
greater angle it subtends ; and,as the apparent diameter 
of the sun, is less in winter than it is in summer, we are 
consequently nearer that body at the former, than we 
are at the latter period. 

2. The sun's diameter forming a different angle with 
us at different times, is a proof that the earth moves 
round the sun in an elliptical,and not in a circular orbit. 

3. The reason why it is hotter in summer when the 
earth is farther from, than it is in winter, when it is 
nearer to the sun, Is, because the sun's rays fall more 
obliquely on us in winter than they do in summer, and 
is also owing to the shortness of the days; just as if 
two persons are sitting near a fire, one who sits before it 
receives the rays perpendicularly, w r hile the other, who 
sits on one side, receives them obliquely; so the former re- 
ceives more heat than the latter, even if he sit at a 
greater distance from the fire. 

18. The appearance of the sun's daily rising 
\n the east, and setting in the west, is occasioned 
by the revolution of the earth on its axis. 

Obs. 1. — This optical illusion may be very readily re- 
conciled, by imagining yourself to be in a coach, and 
looking out at the window, the hedges with their foli- 
age, shrubs, Sec. seem to be in motion, while you imagine 
yourself to be stationary; while it is the vehicle in which 
you are that is moving, and the hedges, trees, &c. which 
are stationary. 
2. This illusion may be farther illustrated, by recollect- 
ing that a person sitting in a boat, and looking steadily 
at the surrounding objects, will apparently observe the 
banks of the water, boats, &c. to be in motion, while the 
boat he is in, is to appearance stationary. 



OF THE SUN. 21 

19. The sun was formerly supposed to revolve 
around the earth, as a centre ; the earth was then 
considered to be the centre of the system now 
called the solar system, but the observations of 
modern astronomers, have proved the sun to be in 
the centre, and the earth, with the other planets, 
to revolve around it. 

Obs. — The direct, retrograde, and stationary appear- 
ance of the planets, prove the planets to revolve around 
the sun. 

20. The sun was also imagined to be a body 
of liquid fire, exhaustless in its nature, which,by 
emitting its rays in every direction, diffused light 
and heat through the system ; but modern astron- 
omers have,with greater plausibility,considered it 
to be a very eminent, large, lucid, solid body, 
shining by its own light, and by the effect or ac- 
tion of its rays upon other substances,causes heat 
and vegetation. 

Obs. 1. — The sun is a solid body,because it revolves con- 
stantly and regularly round its axis,because that axis re- 
mains always in the same position, and because all bodies 
are attracted or gravitate towards it as a centre. 

2. The action of the sun's rays upon substances cans' 
ing heat, may be very readily imagined, by recollecting 
that the collision of a flint against a steel, not only cau- 
ses heat, but produces fire ; and the action of water upon 
lime, not only causes heat, but forces the water to fly oft' 
in steam. 

21. The sun is surrounded by an atmosphere, 
which extends to about 2000 miles from its sur- 
face, but it is at least eighty ti mm denser than 
the atmosphere surrounding the earth. 

22. The disc, or face of the sun is also inter- 
spersed with spots, which appear occasionally, 



22 OF THE SUN. 

varying their number, size, and position. They 
were first discovered by Galileo, and are divided 
into faeculae, or elevations, and macula?, or de- 
pressions of the solar atmosphere. 

23. The particular paths which the plauets re- 
volve in, in going around the bun, is denominated 
the Zodiac. (Plate VII. Fig, 6.) 

24. The zodiac, astronomers have, for con- 
veniency's sake, divided into twelve parts, called 
and marked as follow : namely, Aries V ? Tau- 
rus y; Gemini n ; Cancer 95 ; Leo Si; Virgorn> ; 
Libra =£= ; Scorpio rri ; Sagittarius / ; Capri- 
cornus Vj ; Aquarius %% ; and Pisces ^ ; each 
extending 30°; and they are twelve constellations 
of stars, through which all the planets appear to 
move. 

25. The orbit of the earth is called the eclip- 
tic, and all the orbits of the plauets are imagined 
to cross the plane or level of the ecliptic, in two 
opposite points, called nodes. 

26. The zodiac extends 8° each side of the 
ecliptic, that is, no planet ever recedes farther 
than 8° from the plane of the ecliptic. The 
Dearest distance of any planet, or of any celestial 
body, from the ecliptic, is called its latitude. 

27. When it is noon, or twelve o'clock at any 
place on the earth,the sun is then on the meridian 
of that place ; and, at midnight, the earth's place 
is in the opposite point of the heavens to the sun? 
that is, the portion of the ecliptic opposite the 
meridian at midnight, is the earth's place. 

Obs. — The place of any celestial body as seen from the 
smijis called its heliocentric or true place ; and itsappear- 



OF THE SUNT. 23 



ance, as seen from the earth, is called its geocentric or 
apparent place. 

Obs. 1— (Plate II. Fig. 1.) Let cp . y , n, &c. re- 
present the plane of the ecliptic, let S represent the Sun, 
and the circle a, b, c,the orbit of the Earth, let NEPQ, 
be the meridian of any particular place on the Earth ; 
then, as the Earth derives all its light from the Sun, the 
hemisphere of the Earth represented by AEPB, being 
towards the Sun, will be enlightened, and he would evi- 
dently appear to be in =£= by a spectator on the Earth, 
if =2= were not hidden by his refulgence. This position 
of =23 is called the Sun's place ; and, as the portion or 
hemisphere of the Earth, represented by AEPB, will be 
in the position of ANQJ3 at midnight,the portion of the 
Earth represented by that part, as is evident by the fig- 
ure, is immersed in darkness, excepting such light as is 
derived from the stars and the superior planets; it is evi- 
dent, then, that whatever portion of the ecliptic is op- 
posite the meridian at midnight, is the Earth's place in 
the ecliptic as seen from the sun. 

2. By carefully viewing the same figure, we readily 
perceive, that neither of the inferior planets can possibly 
be seen in the night, but they may be viewed in the 
morning before sun-rising, or in the evening after sun- 
setting. If V represent an inferior planet, as Venus,it 
is evident that the enlightened portion of the Earth is 
always towards that planet, and therefore it is impossi- 
ble for it to be seen from the dark hemisphere of the 
Earth, and consequently no inferior planet can possibly 
be seen in the night, and, therefore, if we see any plan- 
et in the night, it must be a superior planet. 

28. The time the sua appears to be traversing 
around the ecliptic, that is, the time the earth is 
revolving around the sun, is called a year, which 
is 365 days, 5 hours, 48 minutes, and 16 seconds. 

Obs. — The time the Earth is revolving around the Sun 
may be easily observed, by noticing the sign and degree 
of the ecliptic,which is exactly south at midnight.on any 
particular evening, and observing how many days elapse 



24 OF MERCURY. 

before that very sign and degree are in the exact posi« 
tion again. 

29. The sun is beautifully described by Thom* 
-son iu his Seasous. 

" Soul of surrounding worlds ! in whom best seen, 
Shines out thy maker ! may I sing of thee ! 
Tis by thy secret, strong, attractive force, 
As with a chain, indissoluble bound, 
Thy system rolls entire, from the far course 
Of utmost Herschell, wheeling wide his round 
Of eighty years ; to Mercury, whose disc 
Can scarce be caught by philosophic eye, 
Lost in the near effulgence of thy blaze," 

MERCURY. 

30. Mercury is the first planet iu the solar 
system, and the nearest to the sun ; it revolves 
around that luminary with greater rapidity thau 
any other planet, and for this reason the ancient 
Grecian astronomers considered it to be the mes- 
senger of the gods ; they represented it with wings 
at its head and feet, from which is derived ( $ ) 
tiie character used to represent this planet. 

31. The distance of Mercury from the sun is 
37 millions of miles, and it revolves around that 
body in 87 days, 23 hours, 14 minutes, and 33 
seconds. 

32. Mercury is the least of all the planets, its 
diameter being only 3108 miles. 

33. This is called an inferior planet,because it 
is nearer to the sun than the earth ; for this rea- 
son, it is never visible in the night, but on a 
morning, or on an evening, it may sometimes be 



OF MERCURY. 2b 

seen as an attendant on the sun. It revolves on 
its axis in 24 hours, 5 minutes, 28 seconds. 

34. This planet sometimes appears to pass 
across the sun ; it is then apparently like a spot 
on his surface. 

Obs. 1. — This is another proof that this planet's orbit is 
within the orbit of the earth, for if this planet's orbit 
were farther from the sun than the orbit of the earth,the 
sun might transit the planet, but the planet could not 
transit the sun. 

2. The advantages derived to astronomy by the ob- 
servation of transits, are particularly important. By 
them astronomers determine the Sun's horizontal paral- 
lax, or the angle the radius of the earth forms to a spec- 
tator placed at the Sun ; and from the Sun's horizontal 
parallax, they readily determine the distance of the 
Earth from the Sun. 

35. The orbit of Mercury crosses the plane of 
the ecliptic, in Taurus 15°, and in Scorpio 15° ; 
that is, Mercury's ascending node is in # 15°,and 
its descending node in m, 15°. Its greatest elon- 
gation is 28°. 

Obs. — The earth is in & 15° about November 6th, and 
in ni, 15° about May 4th; so when Mercury passes those 
parts of its orbit on these days, it will transit the Sun, 
if it be in its inferior conjunction,or between the Earth 
and the Sun. 

36. Mercury is thus described by Baker : 

" First Mercury, amidst full tides of light, 
Rolls next the Sun, thro' his small circle bright. 
All that dwell here must be refin'd and pure, 
Bodies, like ours, such ardgur can't endure ; 
Our earth would blaze beneath so fierce a ray 
And all its marble mountains melt away." 

3 



26 OF VENUS, 



VENUS. 



37. This is the most brilliant of all the plan- 
ets. When she appears in the morning, she is de- 
nominated the morning star ; and when she is 
visible in the evening, she is called the evening 
star. 

33. Venus is of a beautiful white colour,and so- 
brilliant, as frequently to cause the objects upon 
which she shines to cast a shadow. 

39. Venus is the other of the inferior planets ; 
and as her orbit is within the orbit of the earth, 
she is never visible to us in the night. She turns 
on her axis once in 23 hours, 21 minutes. 

40. Venus is an evening star, or to the east of 
the sun, for 290 days, during which period she 
is poetically called Hesperus, or Vesper ; and 
she is west of the sun during a similar period, and 
is then called Phosphorus, Lucifer, or the Morn- 
ing Star. 

41. The planet Mercury appears to the inhab- 
itants of Venus, in the same situations that Venus 
appears to us, being sometimes a morning, and 
sometimes an evening star. 

42. Venus sometimes transits the Sun, and she 
is then seen as a spot on its surface. The next 
transit of Venus will be on December 8, 1874. 

43. The orbit of Venus intersects the plane of the 
ecliptic in n 15°, or 2 s 15° ; and in f 15°, or 8 s 
15°, which are her ascending and descending 
nodes. 

44. Venus revolves around the sun in 224 



OF THE EARTH. 2? 

days, 1 6 hours, 49 minutes, 11 seconds; at a 
mean distance of 68 millions of miles. When 
viewed through a telescope, she presents phases 
like the moon ; this was first discovered by Gali- 
leo, with a telescope made by him with the bar- 
rel of an organ. The greatest elongation of Venus 
is about 48°. 

45. Venus is thus poetically described by 
Baker : — 

" Fair Venus next fulfils her larger round, 
With softer beams, and milder glory crown'd : 
Friend to mankind ; she glitters from afar, 
Now the bright evening, now the morning star." 



THE EARTH: WITH ITS SATELLITE, OR 
MOON. 



The Distance of the Earth from the Sww, with its 
Shape and Magnitude. 

46. The Earth is the third planet in the solar 
system, and it revolves around the sun between 
Venus and Mars. 

47. The distance of the Earth from the sun is 
95 millions of miles, and in its revolution, is at- 
tended with a satellite or moon, whose office it is 
to reflect to us the light of the sun during the 
gloomy hours of night. 

Obs — The distance of the Earth from the Sun is deter- 
mined in the following manner. 

Plate If. Fig. 2- Let S' represent the Sun ; Pa Sb, a 
meridian of the Earth, O its centre, and acb', a parallel 
of latitude or almacantar : at a the Sun appears in the 



28 OF THE EARTH. 

• 

horizon ; let a S' and S' o be united ; then when S' is in 
the horizon, the triangle S' a u is right-angled at a. 
Then in the right angled triangle, O a S', are given. the 
angle S',equal to 8", equal to the Sun's horizontal paral- 
lax : and the side a o. equal to the serai-diameter of the 
Earth, equal to 3982 miles : to determine the side a S\ 
That is, by trigonometry : as sine ^/ S' : a o : : *ine £ 
S'Oa= j/co-Anej/ S' : a S' — the distance required. 



43. The Earth in shape is round, like all the 
other planets ; the hills and valleys on its sur- 
face, detracting no more from its rotundity, than 
the protuberances in the i ind of an orange, pre- 
vent that fruit from being circular. 

Obs, 1. — That the Earth is round is evident, first,be- 
cause in eclipses of the moon, which are cawsed by the 
moon's passing through the earth's shadow, that shadow 
is circular on the moon's surface, consequently thebo^y 
which casts a circular shadow must be globular, and 
therefore the earth is round. 

2. Another proof of the rotundity of the earth is,that 
it ha* been sailed round by various circumnavigators ; 
they have sailed from particular ports.and by continuing 
their course in one direction, have arrived at the port 
first sailed from. 

The first navigator who sailed round the world, was 
Ferdinand Magellan, a native of Portugal. He sailed 
from Seville in > v pain, on the 10th day of August. l. r >19, 
and performed his voyage round the world in 1124 days, 
arriving at St. Lucar, near Seville, on the first of s ep- 
tember, 1522 He was the first who sailed through the 
Straits which separate Patagonia from lerradel Pnejro, 
in South America ; and they have on that account been 
called by his name, '■* The Straits of Magellan." v ince 
that period, the glohe has been sailed round by various 
navigators, among whom are Sir Francis Drake. Lord 
Anson Capiain Cook, &c. : and this also proves the 
earth to be globular. 

49. The diameter of the Earth is 79G4 miles, 



OF THE EARTH* 29 

and its circumference 25,020 miles, which cir-> 
cumferenee is divided into 360 equal parts, call- 
ed degrees, like the circumference of every cir- 
cle. 

Qbs — The circumference of the earth has been most 
accurately determined by various mathematicians. Our 
countryman, Mr. Richard Harvvood, measured a degree 
between London and York, which degree he found to 
contain 69§ English miles. This distance multiplied by 
$60, gives 25,020 miles for the exact circumference; and 
this, divided by 3*1416, produces T964miles,which is its 
diameter. 

Of the rotary and orbicular Motions of the 
Earth. 

50. The Earth, like all the other planets, has 
a two-fold motion ; it turns round on its axis, 
while it is proceeding gradually in its orbit round 
the Sun. 

61. By the rotation of the Earth on its axis,is 
caused that regular succession of day and night, 
so wisely adjusted by the omnipotent Creator,as 
the seasons for labour and rest. 

52. By this motion, the sun, and all the heav- 
enly bodies appear to approach the horizon, to 
rise, to ascend until they have reached their 
meridian splendour ; to decline ; and, at last, to 
sink in the western sky. 

53. This revolution of the earth on its axis, is 
performed regularly in 23 hrs. 56 m. 4 sec. 

Obs. — The length of the natural day is twenty-four 
hours ; for, while the earth is gradually turning on its 
axis, it is majestically proceeding in its orbit ; therefore, 
the time which elapses from the sun's being on any me- 

3 # 



mV of the earth. 

ridian, on one day, until it appears thereon again, is 
twenty-four hours ; called a natural day. 

54. The motion of the earth on its axis is from 
•west to east ; because stationary bodies, as the 
sun and stars, appear to rise in the east, to attain 
the meridian, and to set in the west. 

55. The axis of the earth is inclined from a 
perpendicular, 231° ; and in consequence of its 
inclination,the day and night are equally divided. 

Obs— To illustrate this, (Plate II Fig. 3.) let S be 
the sun ; E E' the earth in two different positions of its 
orbit ; let P P and P' P' be the axis of the earth in its 
positions E and E', inclined 23 ^° from a perpendicular; 
m n o, m n o, small circles, perpendicular to P P, and 
parallel to each other; T T, T' T', perpendicular to the 
horizon. Now it is evident that the portion of any bo- 
dy, over which a light shines will be enlightened ; and 
this enlightened portion, in a globe like the earth, will 
be one half, or a hemisphere The lines T T, T' S '.which 
divide the light from the dark hemisphere, are called 
terminators. As the parallels m n o are drawn to inter- 
sect T T, T' T', in n, n, &c, so will T T divide m n o 
into two unequal parts, mn,no. 

When the earth is at E,the sun's rays do not enlight- 
ed the north pole P, as is evident by the figure ; conse- 
quently the inhabitants of that region are enveloped in 
darkness, while the inhabitants of the southern regions, 
around the south pole P', have the advantages of contin- 
ual day-light. And the proportion of day to night, on 
any place of the globe, is as the portion of any of the 
parallels m n to n o ; the earth is in this portion of its 
orbit, December 21st. So when the earth is at E' the 
opposite part of its orbit, the noith pole P'. w T iil have 
the sun constantly shining over it, while the south pole 
will he enveloped in gloom ; the earth is so situated on 
June 21st : and as the lengths of the days to the len ths 
of the nights are always as the portions of the parallels 
m n to n o, so they are unequal all ever the earth E,ex- 



OF THE EARTH. 31 

cepting at the eqator, where the terminators bisect the 
axis : therefore the cause of the inequalities in the 
lengths of the day and night, is the inclination of the ax- 
is of the earth, from a perpendicular 23j° to the plane 
of its orbit. 

56. The difFere?it seasons of the year are oc- 
casioned by the different lengths of the days and 
nights. 

Obs. — The longer the days are, at any particular spot 
on the earth, the hotter that spot is ; and the shorter 
the days are, the coider it is ; and as the warm or cold 
seasons are occasioned by the heat or coldness of the 
earth, so those are evidently occasioned by the different 
lengths of the day and night, or, which is the same 
thing, by the inclination of the axis of the earth. 

57. The earth has a motion in its orbit, called 
its orbicular motion, as well as a motion once in 
twenty-four hours on its axis. 

58. This motion in its orbit is progressive,and 
it revolves around the sun, from auy particular 
portion of the ecliptic, until it arrives there a- 
gain, in a year, or 365£ days. 

59. The ecliptic is divided into twelve parts, 
called signs, each containing 30°, and each de- 
gree is subdivided into sixty minutes, and so on. 

Obs.- — The circumference of every circle is divided in- 
to 360°, each degree into 60 minutes, each minute into 
60 seconds, &c. &c. 

60. The motiou of the earth in the ecliptic is 
unequal, owing to its being elliptical. The sum- 
mer half year is therefore eight days longer than 
the winter half year. 

•61. The ecliptic is frequently called the surfs 



32 OF THE EARTH. 



path, because it is the tract he appears to des- 
cribe among the fixed stars. 

62. ft is called the ecliptic, because all the 
eclipses of the sun or moon, happen when the 
moon crosses it, or is nearly in one of those parts 
of her orbit where it crosses it, which points are 
the moon's nodes. 

63. The angle which the ecliptic makes with 
a plane passing through the equator of the earth 
and the sun,is called the obliquity of the ecliptic, 
and is equal to 23^°. 

64. When the earth is in that portion of its or- 
bit where both the north and south poles receive 
the sun's rays at the same time, it is then said to 
be in the equinoxes. This happens when the 
sun enters the constellations Aries and Libra; and 
the first degrees of Aries and Libra are called the 
equinoctial points. The equinoctial points have 
a motion of 501 seconds in a year, backwards, 
or from east to west. This motion is called the 
precession of the equinoxes. 

65. The day is equal to the night all over the 
earth at the time of the equinoxes, which are on 
March 21st, and September 21st; but on every 
day in the year, excepting these two, the day is 
unequal in length to the night all over the 
earth, excepting at the equator,at which place the 
days and nights are always equal. 

66. On the longest day in a northern latitude, 
the sun shines 23^° over the north pole ; and on 
the longest day in a southern latitude, the sun's 
rays enlighten a space of 231° over the south 
pole : these days are Jane 21st, and December 



1>Z.2. 




Fiq.l. 



8 l> 



JP&.4. 



/.' J/.nrr/,-/. 



OP THE EARTH. 33 

21st, called solstitial days : and the portions of 
the ecliptic ia which the earth is, on those days, 
which are 1° of Caacer, and 1° of Capricorn, 
are named solstitial points. 

Obs — The length of the longest day in a northern op 
southern latitude, is equal to the length of the longest 
night ; and when the day is the longest in a northern 
latitude, the day is the shortest in the southern ; and 
when the day is the shortest in a northern latitude, it is 
the longest in a southern. 

67. The earth is in 1° of Aries, on September 
22d ; 1° of Taurus, October 24th ; 1° of Gemini, 
[November 23d ; 1° of Cancer, December 21st; 
1° of Leo, January 21st; 1° of Virgo, February 
19th ; 1° of Libra, March 21st; 1° of Scorpio, 
April 21st; J° of Sagittarius, May 21st ; 1° of 
Capricornus, June 21st; 1° of Aquarius, July 
24 : and 1° of Pisces, August 24th. 

68 The ecliptic being inclined in an angle of 
23|o from the plane of the equator, the earth, in 
passing round the ecliptic, must be at different 
distances from the plane ; the nearest distance 
from the plane of the equator to the sun is the 
earth's declination, commonly called the sun's de- 
clination. 

Obs —To illustrate this, (Plate II. Fig. 4.) let AGB 
FC be the plane of the equator and the pun ; A £' B D 
C the ecliptic, intersecting the former in B and A, ma- 
king the angles DBF ; D C F : G A E' ; E' B G,each 
equal to 23^° ; imagine the points A C to be united, so 
shall <\ GBCiAF/BDCbe two circles. Now when 
the earth is at A and B, it has no declination, the days 
and nights are then equal all over the earth,which hap- 
pens on March 21st and September 21st, the day and 
night each being equal to 12 hours. Let the earth be 
at £, any particular situation of the ecJiptic, then the 



34 OF THE EARTH. 

perpendicular E e being drawn, E e being the nearest 
distance from E to any part of ABC, is the earth's decli- 
nation when it is at E; let E be placed in what part so- 
ever it may of AEBDC. When the point E 
coincides with D, the declination is the greatest, and D 
F is equal to 23^°, equal to the angle D B F. 

69. The declination is the greatest at the sol- 
stices ; and the least,or nothing, in the equiuoxes. 

Divisions of the Earthy or the Jive Zones explain- 

cd. 

70. The inclination of the axis of the earth, 
causes the sun not to shine on a certain portion 
of its surface at one season of the year ; this por- 
tion of the earth is called a frigid zone. 

71. As the earth has at one season of the year, 
a portion of its surface, extending 23^° from the 
north pole ; and at the opposite season, a similar 
portion of its surface, surrounding the south pole, 
deprived of the rays of the sun ; there are con- 
sequently two frigid zones. 

72. That portion of the earth which receives 
the rays of the sun in a perpendicular direction, 
is called the torrid zone. This zone extends 231° 
each side of the equator, making an extent of 
47° in breadth. 

73. The portions of the earth w 7 hich every day 
in the year are enlightened with the sun^ rays, 
but which never shine perpendicularly thereon, 
are called temperate zones. There are two tem- 
perate zones, and the whole number of zones 
is five ; namely, one torrid, two temperate, and 
two frigid. 



OF THE EARTH. 35 

74. The circles which bound the torrid zone, 
are called tropics ; that bouuding it on the north, 
is called the tropic of Cancer, and that bounding 
it on the south, the tropic of Capricorn. 

75. The circle which bounds the north frigid 
zone, is called the Arctic circle, and that which 
bounds the south frigid zone, the Antarctic cir- 
cle ; these circles are frequently called Polar 
Circles. 

The Atmosphere of the Earth with its various 
Phenomena. 



76. The earth is surrounded with a thin, elas- 
tic, transparent, and invisible fluid, called the 
Atmosphere. 

77. The Atmosphere contains within itself the 
principles of life and animation, as none of the in- 
habitants of the earth, not even vegetables could 
exist, without enjoying its genial influence. 

78. It extends to about fifty miles from the 
earth's surface, and the further it is therefrom, 
the more rare and thin it gets. 

79. The atmosphere is not only essential to us, 
by its containing the principles of life, but it is 
necessary for our comfort, by causing the light 
of the sun to be seen after he has descended the 
western, and before he arises in the eastern hori- 
zon. This faint light before sun-rising, and 
after sun-setting, is called the Crepusculum, or 
the Twilight. The twilight commeuces in the 



36 OF THE EARTH. 

morning, and ends in the evening, when the sue 
is 18° perpendicularly below the horizon. 

80. The eartli is not only surrounded, but eve- 
ry square inch of its surface is pressed by the at- 
mosphere, with a power of fourteen pounds and a 
half. 

81. The atmosphere is the grand source of 
rains and of dews, which moisten and fertilize the 
earth. Without it there would be no day, as the 
sun would, without the atmosphere, appear an im- 
mense large fiery globe where he was visible, 
and the places on which his rays did not shine, 
would be immersed in gloom. 

82. The atmosphere attends the eartli ia its 
motions, and its gravity is about a thousand times 
lighter than water. 

83. The air being acted upon by the attrac- 
tions of the sun and moon, has tides generated in 
it, just as the sea has, and this is probably the 
reason, why its temperature is more changeable 
at the new and full moon, than it is at other 
times. 

84. The air is rarefied by heat, and condensed 
by cold ; that is, the same quantity of air will 
occupy a greater or lesser space,according to its 
density. 

Ohs. — This may be very easily proved, by fiUing a 
bladder with air. ar.d tying its neck so secure that none 
may escape ; if this bladder be exposed to the heat of 
lire, it will, as the air contained therein rarefies, expand 
the bladder, and at length burst it with a great report. 

85. The atmosphere is likewise essential to 
the inhabitants of the earth, by rarefying and 



OF THE EARTH. 37 

sustaining the various effluvia emitted from its 
surface. 

Obs. — The various noxious vapours which are gener- 
ated on the earth, ascend through the atmosphere,until 
they arrive at that part, the specific gravity of which,is 
equal to the specific gravity of the ascending vapours. 

Bd. The various vapours and effluvia which 
arise from the earth, float in the atmosphere, and 
are called clouds ; and they are of different 
heights, according to their specific gravity or 
weight. Clouds are scarcely ever more than two 
miles high, and very frequently not more than five 
or six hundred yards. 

87. The diversified shapes of the clouds is 
owing to their loose texture, and their different 
colours are occasioned by their particular situa- 
tions with regard to the sun, combined with the 
quantity of aqueous particles they contain. 

Obs.— The altitude of any particular cloud may very 
easily be ascertained, thus,— 

Plate III. Fig. 1. Let C be any particular part cf a 
cloud ; let A and B be any two stations on the earth ; 
let two people at the same instant take the measure of 
the angles CAB and CBD. Then, in the trianjrle ACB, 
are given AB and all the angles, to find BC ; and in 
the triangle BCD are given all the angles, and BC, to 
hndDC, which will be the heightof the cloud required. 
Ihus if the angle A be 35°, the ,/CBD=54<\ and the 
distance AB880 yards; the altitude of the cloud DC= 
936 yards nearly. 

88. When the clouds are increased by a con- 
tinual addition of vapours, and their particles are 
driven close together, by the force of the sur- 
rounding atmosphere, they have a very dark ap- 

1 



3B OF THE EARTH. 

pearance and are generally very low : and when 
they are too heavy for the atmosphere to sustain, 
they descend copiously on the earth in drops of 
rain. 

89. The drops of rain increase in size and mo- 
tion in their descent; so that a bowl plac- 
ed on an emiuence, will receive a considerably 
less quantity ofrain,than one placed on the earth's 
surface, during the same shower. 

90. The atmosphere is also the grand reservoir 
of dews, which so liberally replenish the earth ; 
and in many countries, as Chili, Egypt, &c,sup- 
ply the want of rain. 

91. The dew does not descend from the clouds 
in the same manner as rain; but as the rays of the 
sun heat the earth; so, when he has declined the 
western horizon, a number of particles evaporate 
from its surface,and ascend into the surrounding 
atmosphere, where the coolness of the air con- 
denses them, and causes them to fall in very mi- 
nute drops ; and thus is formed that universal 
means of fertility, dew. 

92. The hotter the day has been,the more par- 
ticles will evaporate in the night, and consequent- 
ly the heavier will be the dew. This is the rea- 
son why the dews are greater in hot countries, 
than they are in cold ones. 

93. When the atmosphere is filled with va- 
pours, and a cold breeze arises, which prevents 
their ascending and uniting, clouds are formed 
in the lower parts of the atmosphere, which low 
clouds are called mists or fogs. 

Obs. — The earth is generally accompanied with a mist 
on a cold morning, but as the rays of the sun begin to 



OF SNOW, HAIL, LIGHTNING, &C. 39 

enlighten and warm the atmosphere, it disperses, and 
forms clouds in the higher regions of the air. 

OF SNOW, HAIL, LIGHTNING, THUNDER, 
FALLING STARS, AND THE AURORA BO- 
RE ALIS. 

94. When the clouds are frozen before their 
particles are united into rain, small portions of 
them being united and made heavier by such 
condensation,they will descend in flakes of snow. 

95. Hail is a compact mass of frozen water, 
consisting of drops of rain frozen in their descent 
from the clouds to the earth. 

96. As the atmosphere is the receptacle of all 
the effluvia which rise from the various bodies 
on the earth's surface ; so, when clouds com- 
posed of nitrous and sulphureous substances meet, 
they produce a strong conflict, and fire is emit- 
ted therefrom, which is called lightning. 

97. The noise accompanying this ignition of 
sulphureous substances is called thunder; and the 
clouds being thus decomposed, torrents of rain 
generally follow. 

Obs. — The distance we are from the clouds, from which 
the lightning proceeds, may be very readily calculated. 
For as sound moves 1J42 feet in a second,if the number 
of seconds elapsing between the sight of the lightning, 
and the report of the thunder be multiplied by 1142, it 
will give the distance of the cloud required, in feet. 

98. When the clouds which thus explode are 
very low, steeples, high trees, or any thing that 
stands in a prominent situation, is liable to be in- 
jured or destroyed by the ignited particles. 



40 DIVISIONS OF THE BODY OF THE EARTH. 

99. The atmosphere is likewise interspersed 
with vapours, which coalesce according to their 
nature. Some of the particles appear like stars, 
and fall from a higher to a lower situation, and 
are then called falling stars. 

100. The aurora borealis is supposed to be oc- 
casioned in the higher portions of the atmosphere, 
where there are particles of inflammable matter, 
which are ignited by electricity. 

THE DIVISIONS OF THE BODY OF THE 
EARTH. 

101. The solid body of the earth is divided in- 
to three sections, viz — First, the exterior ; sec- 
ondly, the interior; and thirdly, the middle sec- 
tion. 

102. The exterior portion is the part on which 
vegetables, plants, trees, fruits, &c. &c. are gen- 
erated and grow : this is wisely ordered by the 
great Creator, for the support of its numerous in- 
habitants. 

Obs. 1. — The external or corticle part of the earth is 
composed of hills, valleys, mountains, and plains, and 
with various beds or layers of strata, which are gener- 
ally interspersed with respect to each other, according 
to their specific gravity or weight, the heavier being 
below, and the lighter above. 

2. These inequalities in the surface of the earth are 
supposed to have been occasioned by the concussion and 
agitation of the various parts of the earth, at the uni- 
versal deluge, when the world seems to have been con- 
vulsed ; but as the water subsided, and flowed into the 
deepest pits,the other portions of matter were collected 
together, according to their specific gravities. 



OF TIME. 41 

103. The middle or intermediate portion is 
possessed by fossils, as quarries of stones, mines of 
metals, salt, coal, &c. &c, all necessary for the 
comfort and convenience of mankind. 

104. The internal portion of the earth is sup- 
posed to be composed of a solid mass of different 
sorts of metals, stoues,&c, but which can never 
be explored by human labour. 

O65. — That the internal portion of the earth contains 
metals in very great proportion is very plausible, for the 
eminent Dr. Hutton, from many ingenious experiments, 
proves the mean density of the earth to be£ as heavy 
as common stone ; its interior must, therefore, be com- 
posed of substances of very great density ,which we have 
every reason to conclude is metal. 

OF TIME. 



Of the Natural, Astronomical, or Solar Day ; of 
the Sidereal Day : and of the Equation of 
Time. 

105. The period the earth takes to revolve on 
its axis, that is, one revolution of the earth,is call- 
ed a day. 

106. The day has been divided by mankind 
into 24 parts, called hours, each hour into 60 
parts, called minutes ; each minute into 60 sec- 
onds, and so on to thirds, fourths, &c. &c. 

107. This period of 24 hours is called a solar, 
astronomical,civii, or natural day, because it is the 
time which elapses between the sun's being op- 
posite any meridian, before it appears to return 
to the same meridian again. 

4* 



42 OF TIME. 

108. The sidereal day is the time which elap- 
ses between the appearance of any fixed star on 
any meridian, until its apparent return to the 
same again, and consists of 23 hours, 56 minutes, 
4 sec. 1. 

109. The sidereal day is the exact time the 
earth takes to revolve on its axis, and is deter- 
mined by observing the period which elapses be- 
tween the same fixed star coming twice to any 
particular meridian. 

110. The difference between the solar and si- 
dereal day, is the time (or distance reduced from 
time) the earth proceeds in the ecliptic in one 
revolution on its axis. 

111. Because the earth moves in an elliptic, 
and not in a circular orbit, its motion in some 
parts of that orbit is quicker than it is in other 
parts; and, as the solar day is the time of the 
sun's appearing on any meridian, to its apparent 
return to the same again, the solar or natural day 
is consequently shorter at some seasons of the 
year than it is at other seasons. 

Obs. 1. — The earth (as well as the other primary plan- 
ets) moves round the sun in an elliptic, and not in a 
circular orbit, having the sun fixed in a focus, and the 
secondary planets revolve around their respective pri- 
mary planets likewise in elliptic orbits ; the primary of 
each being in a focus of the ellipse, the secondary des- 
cribes. 

2. (Plate III. Fig. 1.) If S represent the sun, g f e\ 
&c. &c. the elliptic orbit of the earth. The spaces or ar- 
eas g S f, f S e',&c. described by the earth in equal times, 
are equal, (this motion of the earth was first discovered 
by Kepler,a very eminent astronomer of Germany.) And 
as these areas will depend in some measure on the length 
of the lines Sg, Sf, Sa, Sb, &c. the length of the curves 
gf, f e', e' a,&c. will be longer or shdrter,Vs the distances 



TZ.3. 




OF TIME. 43 

t>S, aS, fS, &c. are increased or diminished ; and if we im- 
agine the spaces a e', e' f, f g, &c. to be passed over by 
the earth in a day, the inequality in the lengths of the 
solar days may be very easily conceived. 

112. Astronomers consider the period the earth 
is revolving around the sun, to be equally divi- 
ded into hours ; twenty-four of which they 
call a day ; this is called mean time, or the time 
shown by a well regulated clock. 

113. The difference between meantime, or 
the equal division of the year ; and the solar day, 
or the time which elapses from the sun's being on 
one meridian, to its appearance there again, is 
called equation of time. 

114. The time shown by a good sun-dial is 
solar time, and if to -that we add or subtract the 
equation of time, we shall have mean time. 

Obs. 1. — In common language, a day is the term ap- 
plied to the space of time between the rising and setting 
of the sun. This is an artificial day. 

2. The astronomical day commences at noon, and is 
reckoned onward regularly until the noon following. 

S. From noon to midnight the hours are frequently 
distinguished by the letters P. M., and from midnight 
to noon by A. M. 

4. The day begins with different nations at different 
times. England, France, Spain, and other parts of Eu- 
rope begin their day at midnight. In some parts of 
Germany and Italy they begin their day at sun-setting, 
and reckon onward until the sun sets again ; so did the 
Jews, the Romans, and the Turks. The Babylonians 
began their day at sun-rising. 




OF THE MOON. 
THE MOON. 




The Offices, Distance, Magnitude, &c. of the 

Moon. 

(Plate IV. Fig, 1.) 

115. Next to the sun, the moon is the most 
splendid and brilliant orb we observe in the heav- 
ens ; and, by her dissipating the gloom of dark- 
ness, she is not only a pleasing, but a welcome 
and useful companion in our tedious nights, 

116. The moon is a solid opaque body,having 
no light of her own, but reflecting the light she 
derives from the grand luminary of day ; and she 
is like all the other planets, of a globular form. 

117. The moon is a satellite, or secondary 
planet of the earth, revolving around it in the 
same manner as the earth revolves around the 
sun, in an elliptic orbit, the earth being in a fo- 
cus of the elliptic curve. 

118. The moon, to a spectator ignorant of the 
celestial bodies, is considered one of the largest 
in the heavens, but it is her comparative nearness 
to us, which causes her to appear so large and 
bright. She is 2161 miles in diameter. 

Ohs — The diameter of the moon is ascertained thus ; 
The moon's diameter to a spectator on the earth makes 
an angle of 31' 7". 

(Plate III. Fig. 3.) Let E represent the earth, AB 
the diameter of the moon, AE=BE=the moon's dis- 
tance from E the earth. 180-— 31' 7" 

Then the ^EAB=: =*89° 



TIBDE COQUET ©IP 181$) > /Fig 1- 



TZ * 




TIEEE. FIDOS' AS SEEJ TIER OTT GZEL A. TZEZLESCQIKE > 



M?.-2. 



JRJIditireriek sc. 



OP THE MOON. Ab 

44' 26 J^srr^EBA. And in the triangle EAB.are giv- 
en Z ABE =i /BAE ami AE; to find the side AB; that 
is, as S /EBA. : AE : : &/_ E : AB, as required. 

119. The axis of the moon is inclined from a 
perpendicular 1° 43' to the plane of its orbit. 

120. The distance of the moon from the earth 
is 240,000 miles. 

Obs. — The distances of any of the planets,or the moon, 
from the earth, is readily ascertained by their horizon- 
tal parallaxes, in the same manner as the distance of the 
earth from the sun is determined by the sun's horizontal 
parallax. 

Of the orbicular and rotary Motions of the 
Moon. 

121. The motion of the moon round the earth 
is from west to east, in the same direction as the 
earth revolves arouud the sun. 

Obs. — This fact will appear evident by observing a so- 
lar eclipse, which is occasioned by the moon's parsing be- 
tween the earth and the sun ; the western edge of the 
sun will be first obscured, and the eastern edge last; con- 
sequently the motion of the moon must be in that direc- 
tion, or from west to east. 

122. The moon makes a complete revolution 
around the earth in 29 days, 12 hs. 44 min., and 
this is the time from one new moon to another, 
called a synodical month, or lunation. She re- 
volves on her axis exactly in the same time, and 
this period is therefore the length of her day. 

Obs. — This is proved by observing the spots on her 
surface: as they always appear in the same position,it is 



46 OV THE MOON. 

therefore evident that she turns on her axis in the same 
time she revolves around the earth. 

123. As the earth turns round daily on its ax- 
is, the inhabitants of the moon will distinctly see 
the mountains, islands, &c. on the earth, as so 
many spots on its surface. 

Obs. — The utility of the appearance of these spots, to 
the inhabitants of the moon, will be to measure their 
time, and will serve them the same purpose as a sun- 
dial serves us. 

1 24. The time the moon is revolving round 
her orbit, from any fixed star, until it arrives at 
the same again, is 27 days, 7 hs. 43 min. 8 sec. ; 
this is called a periodical month. 

Obs. — The reason why the synodical is longer than 
the periodical month, is, because while the moon is re- 
volving round the earth, the earth is proceeding round 
the sun ; so that from one conjunction of the sun and 
moon to another conjunction,the earth has moved about 
one-sign, or 30° in the ecliptic ; consequently 1_?_ per- 
iodical month is nearly equal to a synodical month. 

Of the various Appearances of the Moon. 

1 25. At the time of the new moon, she is then 
directly between the earth and sun ; this is call- 
ed a conjunction of the sun and moon, and is 
marked 6 ; she is then at her nearest distance to 
the sun. 

Obs -—(Plate V. Fig. 1.) The moon has been beauti- 
fully described by Pope in his translation of the Iliad of 
Homer : — 

When the full moon, refulgent lamp of night, 
O'er heavVs clear azure spreads her sacred light; 



OF THE MOON. 47 

When not a breath disturbs the deep serene, 
And not a eloud o'ercasts the solemn scene ; 
Around her throne the vivid planets roll, 
And stars unnumberM gild the glowing pole. 
O'er the dark trees a yellower verdure shed, 
And tip with silver ev'ry mountain bead ; 
Then shine the vales, the rocks conspicuous rise, 
A flood of glory bursts from all the skies ; 
The conscious swains rejoicing in the sight, 
Eye the blue vault, and bless the useful light. 

126. At the time of full moon the earth is be- 
tween the sun and moon ; she is then said to be in 
opposition to the sun, which opposition is mark- 
ed <? : she is then at her greatest distance from 
the sun. 

127. The conjunction and opposition of the 
moon are very frequently called syzygies. 

128. As the moon derives all her light from 
the sun, she has, at her conjunction, her dark 
hemisphere toward the earth, while her enlight- 
ened portion is toward the sun ; she is then invis- 
ible to us ; but at the time of her opposition her 
dark hemisphere is from the earth, and her en- 
lightened portion toward the earth, as well as to- 
ward the sun. 

129. At the full moon, she appears to rise as 
the sun appears to set, and to come on the merid- 
ian at midnight ; majestically declining, she de- 
scends the western horizon, as the sun ascends 
the eastern. 

130. The various appearances of the moon 
from new to full moon, are called phases,and are 
occasioned by a smaller or greater portion of her 
♦enlightened surface being visible by us. 



48 OF THE MOON. 

131. As the moon increases from her conjunct 
tion to her opposition, she will present to our 
view a variable portion of a circle, the visible 
portion of the circumference of which will be to* 
ward the west. 

132. When she arrives half way between her 
conjunction and opposition, she appears like a 
semicircle ; when increasing, or in her first quar- 
ter, the visible portion of her circumference is 
toward the west, and when decreasing towards 
the east. * 

Obs. 1. — As the moon revolves around the earth, the 
ear'h, to the inhabitants of the moon, appears to revolve 
around her. The earth appears above their horizon the 
period of one half a lunation, and the period of the oth- 
er half it is invisible to them. The earth is the largest 
and most beautiful object in the heavens to them ; and 
by transmitting the sun's rays, dissipates the gloom of 
their night. 

2. At a new moon, the sun is visible to one half ofthe 
moon, and the earth shining in full splendor, visible to 
the other half: and at a full moon one half of the moon 
is immersed in darkness, while the other half is enlight- 
ened by the sun. The earth presents to the moon the 
same kinds of phases that she presents to the earth, only 
the phases ofthe earth are considerably larger and more 
resplendent. 

1 33. As the moon revolves around the earth in 
29 days, 12 lis. 44 min., and as the circumfer- 
ence of her orbit is 360°, her mean motion is 12° 
1 1' each day. 

134. The orbit ofthe moon makes a variable 
angle from 5° to 5° 18' with the plaue of the 
ecliptic. The two points where her orbit is im- 
agined to cross the ecliptic are called the moon's 
nodes. 

135. The moon's nodes move retrograde, or 



OF THE MOON. 49 

contrary to the order of the signs, 19° 19' 44" 
every year, 

136 When she appears to pass over any plan- 
et or star, such plauet or star is said to suffer an 
occultation. The occultations of the stars are 
useful in determining the longitudes of places, in 
the same manner as eclipses of the moon are. 

Of the Spots or Mountains of the Moon. 

137. The surface of the moon is interspersed 
with hills, valleys, volcanoes, &c. like the earth, 
to which astronomers have, for convenieucy's 
sake, given names. The altitudes of the lunar 
mountains have been determined by Dr. Her- 
schell and others, by means of their shadows, on 
the surface of the moon. 

138. The moon is surrounded with an atmos- 
phere; but it is much rarer than the air encom- 
passing the earth, her enlightened surface being 
always visible through it. 

139 Any terrestrial body being removed to 
the moon, would only weigh one third as much 
as it dees at the surface of the earth ; therefore 
the moou's atmosphere must be at least three times 
rarer than our air. 

The Harvest and Horizontal Moon. 

140. The full moon, which happens at, or near 
the autumnal equinox, is called " The Harvest 
Moon," because it rises for several evenings fol- 



5 



50 OF MARS. 

lowing nearly at the same time : by which means 
it diffuses its cheering light, to aid the husband- 
men to gather in the harvest. 

Obs, — This is occasioned by the ecliptic's (and conse- 
quently the Moon's orbit) making the greatest angle 
with the horizon at that season. 

141. The moon and all the heavenly bodies, 
appear larger when near the horizon, than they 
do as they ascend towards the zenith. This ap- 
pearance of the moon is denominated "The Hori- 
zontal Moon." 

MARS. 

(Plate Y. Figs. 2. and 3.) 
142* Mars is the fourth planet in the solar sys- 
tem, and is situated between the orbits of the 
earth and Jupiter. 

143. This is in appearance the darkest and 
least splendid of all the planets ; it is of a dusky 
red hue. Bright spots have been observed near 
its poles, which are supposed to be occasioned by 
those regions being covered with ice or snow. 

144. The dusky red appearance of Mars, is, 
according to many astronomers, owing to a thick 
atmosphere with which it is surrounded. 

145. From the red appearance of this planet, 
it is denominated Mars, or the God of War, and 
is represented by this character % , denoting a 
mau with a spear in his hand. The same char- 
acter is used to represent iron among metals. 

146. Because Mars is sometimes opposite the 
meridian at midnight, his orbit is evidently out- 
side the orbit of the earth, (Obs. 2. Art. 27.), and 
he is the nearest of the superior planets. 



1>Z.J. 



v 'X^l 




"^iiimi: 



Fia.l. 



o 

• d o 




d o 



d ^ 9 
m 9 o 



^>^. #. 



^•«* 





Fi^.l. T/ie JViases of tfte Jlfoo/i. 
JFrty. 2. and 3. J%e Te/escopic ^4ppea7*a?zces afJJfars . 



OF JUPITER. 51 

147. The distance of Mars from the sun is 145 
millions of miles. His orbit makes an angle of 
1° 52' with the plane of the ecliptic. 

148, Mars is 686 days 23 hours revolving a- 
round the sun : he turns on his axis in 24 hours 
40 minutes: this Dr. Hook and Cassini first dis- 
covered by the gradual motions of his spots. 
His axis is inclined from a perpendicular, 59°22' 
to the plane of his orbit. 

149. The diameter of Mars is 4444 miles. The 
place of his ascending node is # 17° 17',and that 
of his descending node r^ 1 7° 1 7'. His horizon- 
tal parallax is 30'' from which his distance from 
the earth or sun is readily determined, (See 
page 79.) 

150. The analogy between Mars and the 
Earth, is by far the greatest of any two planets 
in the whole solar system. 

151. The inhabitants of Mars have three in- 
ferior planets, Mercury, Venus, and the Earth. 
Each of these will sometimes be a morning, and 
sometimes an evening star; although the Earth 
will be the brightest and the most luminous ob- 
ject they can behold. 

JUPITER. 
(Plate YJ. Fig. 1.) 

152. Jupiter is the fifth planet in the solar 
system ; it is situated between the orbits of Mars 
and Saturn, at a distance of 490 millions of miles 
from the snn. 

153. This is the largest planet in the solar 



52 OF JUPITER. 

system, its diameter being 90,145 miles ; it is in 
appearance of a beautiful bright, white lustre,and 
on that account is denominated a morning, or an 
evening star, according as it is west or east of 
the sun. 

154. This planet for his superiority among the 
planets, is called Jupiter, as he was the might- 
iest of the heathen deities. He is represented 
by this character % , to denote his whiteness ; 
the same is used to distinguish tin among metals* 
155 Jupiter revolves around the sun in 11 
years, 314 days, or 4332 days. Its orbit makes 
an angle of 1° 20' with the plane of the ecliptic. 

156 Jupiter's ascending node is 8° ofss, and 
his descending node 8° of VJ. 

157. The sun appears to us nearly five times 
as large as it does to the inhabitants of Jupiter , 
consequently they receive only one twenty-fifth 
part of the light and heat we derive from that 
luminary. 

158. To compensate for this defect of light, 
our bounteous Creator, who is ever attentive to 
the comforts of His creatures,has accommodated 
Jupiter with four satellites or moons, which ma- 
jestically revolve around it, and thus cheer their 
gloomy nights. 

159 The night, to the inhabitants of this su- 
perior planet, is never so long as five hours, be- 
cause it revolves on its axis in 9 hours 56 min- 
utes. 

1 60. The axis of Jupiter is nearly perpendic- 
ular to the plane of its orbit, consequently the 
length of its days and nights are nearly equal all 



THE SATELLITES OF JUPITER. 53 

over its surface ; this is another wise provision of 
its Creator, for if its axis Avere much iQclioed,one 
portion of its body would alternately, be depriv- 
ed of the sun's light, and have constant day, for 
nearly the space of six years. 

161. The surface of Jupiter appears to be in- 
terspersed with various streaks, which are called 
belts ; they are parallel to its equator, though 
they frequently change their situation : they are 
thought to be clouds floating in its atmosphere ; 
its surface is also interspersed with spots. 

The Satellites of Jupiter, 

162. The satellites of Jupiter are too minute 
to be observed by the naked eye, but with a tel- 
escope they present a very majestic appearance. 

' Obs. — The satellites of Jupiter remained undiscovered 
in the earlier ages of astronomy, when the science was 
cultivated without the assistance of magnifying glasses ; 
but, in the year 1609, by the help of a telescope, Simon 
Marius, a German mathematician, first discovered these 
satellites, and, in the ensuing year, they were observed 
by Galileo. 

163. The advantages which are derived to as- 
tronomy from this discovery are very considera- 
ble ; their eclipses prove that light is progress- 
ive in its motion, and does not arrive to us from 
the sun instantaneously, as was formerly suppo- 
sed. 

Obs. — When Jupiter is in that portion of his orbit 
which is nearest to the earth,the eclipses of his satellites 
are seen about eight minutes sooner than they are when 
Jupiter is in that portion of his orbit which is farthest 

5* 



54 SATURN, AND HIS SEVEN SATELLITES. 

from the earth ; so that light moves 190 mil lions of miles 
(the diameter of the earth's orbit) in 16 minutes, or 
about 12 millions of miles in a minute. 

164 Aoother advantage derived by the eclip- 
ses of the satellites of Jupiter, is the determination 
of the longitu te of any place on the earth, where 
such eclipses are observed. 

Obs. — If two persons at different places on the earth, 
observe the eclipsing of any particular satellite, the dif- 
ference in the time of observation, reduced into degrees, 
by reckoning 15° for one hour, gives the difference of 
longitude of those places. 



SATURN, AND HIS SEVEN SATELLITES. 
(Plate VI. Fig. 2.) 

165. Saturn was formerly considered the most 
distant planet in the solar system ; he is expressed 
by this character \i , denoting an old man sup- 
porting himself upon a staff. The same character 
is used to characterise lead among metals. 

1 66. Saturn, to the naked eye, appears like a 
star of the second magnitude? it is 10,759 days, 
or nearly 30 years revolving around the sun,at a 
distance of 908 millions of miles from that lumi- 
nary. 

167. The diameter of Saturn is 77,950 miles; 
he has seven moons constantly attending him, and 
his body is circumscribed by a luminous double 
ring. 

163. The surface of Saturn is likewise be- 
spangled with various belts, like the belts of 



The Planet Jupiter Avith his four Satellites, as seen through a Telescope 




The Vianet Saturn .with his seven Satellites, as seen through a Telescope. 



HERSCHELL, WITH HIS SIX SALELLITES. 55 

Jupiter, and spots, by which astronomers have 
found that he revolves on his axis in 10 hours 16 
minutes. 

169 The orbit of Saturn makes an angle of 
2° 30' with the plane of the ecliptic. The place 
of his ascending node is 22° of 25, and the place 
of his descending node is 22° of >J« 

1 70. The ring of Saturn is a broad circular 
arch, encompassing the body ot the planet, with- 
out touchiug it, somewhat similar to the wooden 
horizon of an artificial globe. The ring was first 
discovered by Galileo in the year 1 609. 

171. Five of the Satellites of Saturn were dis- 
covered by Cassini and Huygens, and the last 
two, being the nearest to the planet, by the emi- 
nent Dr. Herschell with his majestic teles- 
cope, which magnifies not less than six thousand 
times I 

1 72. The ring of Saturn appears to be a solid, 
encompassing the planet, because it has a motion 
on its axis, and casts a shadow on the surface of 
the planet. 

[HERSCHELL, WITH HIS SIX SATELLITES, 

1 73. The Herschell planet was discovered by 
Dr. Herschell, at Bath, on March 13, 1781, near 
the foot of Castor ; and, from its discoverer, has 
derived its name. The character by which it is 
distinguished is $ . 

174. The distance of Herschell from the sun, 
is 1813 millions of miles; and it requires 31,346 



56 FLUX AND REFLUX OF THE TIDES. 

days, or nearly 86 years to revolve around the 
sun* In appearance it is about the size of a star 
of the sixth or seventh magnitude. 

175. The diameter of this planet is 34,404 
miles ; and, in its progress round the sun, it is at- 
tended by six satellites or moons. 

176. This planet is by many astronomers call- 
ed Uranus, because as Mars was the son of Jupi- 
ter, so Jupiter was the son of Saturn, and Saturn's 
father was named Uranus among the heathen dei- 
ties. 

Obs. — HerschelPs ascending node is 2 s . 12°, or 12° of 
H, and bis descending node 8 s . 12°, or 12° of / ; and 
his orbit is nearly parallel to the ecliptic,forming only an 
angle of 46' therewith. 

ASTEROIDS. 

177. There are four smaller planets between 
the orbits of Mars and Jupiter, called Asteroids: 
they were so named by Dr. Herschell. 

178. The asteroids are called Vesta, Juno, 
Ceres, and Pallas; they are about the siae of our 
moon, and revolve around the sun in four years 
and eight months, at a distance of 288 millions of 
miles. 

1 79. These Asteroids are invisible to the naked 
eye ; their theories are very little known. 

OF THE FLUX AND REFLUX OF THE TIDES. 

180. A tide is that motion in the seas or riv- 
ers, by which they rise and fall in regular suc- 
cession. 

181. This motion of rising and falling is occa- 
sioned by the mutual attractions of the sun and 
moon upon the water. 



COMETS, 



57 



182. There are two tides id the space of twen- 
ty-five hours ; or it is high water at any place 
once in about twelve hours and a-half. 

183. At the conjunction of the sun and moon, 
both these luminaries are on the same side of the 
earth, and by their united attractions upon the 
same portions of the water, conspire to elevate its 
surface more than at other times ; so, when the 
sun and moon are in opposition, the sun by his 
influence raises the water on one side of the earth, 
at the same time that the moon elevates it on the 
opposite side. 

184. The mean attraction of the moon in ele- 
vating the water to that of the sun, is as five is to 
one, and the nearer these bodies are to the earth, 
the higher will be the tides. 

Obs. — The lowest tides happen when the moon is in 
her quadratures, and the highest when she is in her syzy- 
gies, or about two or threedays after. Lakes have no 
tide:-, because every portion of their surface is attracted 
alike. 

COMETS. 

(Plate TV. Fig 1.) 

185. There are other celestial bodies besides 
planets,which traverse infinite space, called Com- 
ets, and are known from the planets by their be- 
ing attended with a luminous tail, iu a direction 
opposite the sun, 

186. Comets revolve around the sun in very 
eccentric orbits, in some part of which, they are 
frequently as near the sun as Mercury, and at 



58 - COMETS. 

the opposite part, even farther distant than Her- 
schell. 

187. Comets were formerly considered as su- 
pernatural agents, sent by the incensed Deity as 
omens of plagues, pestilences, famines, and other 
scourges of mankind,for crimes committed against 
the Divine Being. 

Obs> — 'Their nature being now better understood, they 
are no longer terrible ; but as there are many illiterate 
people who still think them warnings of portending evils 
to mankind,it may not be improper to remember,that the 
great Architect of the universe has formed every part of 
his creation according to his own infinite wisdom, in di- 
vine and perfect order, and subjected all to laws and reg- 
ulations. He does not hurl worlds at random through 
infinite space, or permit any portion of his works to be 
affected by fortuitous circumstances. Religion glories 
in the test of reason, of knowledge, and of true wisdom ; 
it is every where connected with,and elucidated by them. 
From philosophy we may learn, that the more the works 
of our benign Creator are contemplated,the more he must 
be adored; and his government and superintendence over 
every portion of his creation will be evinced." 

188. Tycho Brahe, a Danish astronomer, was 
the first who restored comets to their true rank 
in the creation, by assigning them their situation 
in the solar system. 

189. Sir Isaac ^Newton says, Comets are com- 
pact, solid, and durable bodies, moving in very 
oblique orbits, and their tails are a very thin and 
slender vapour, emitted by the head or nucleus 
of the comet, ignited or heated by the run's rays. 
They are only visible to us when tbey are in 
that portion of their orbit nearest to the sun. 



OF THE FIXED STARS. 59 

190. The periodic times of the greater num- 
ber of the comets are uncertain. One is' known to 
be 76 years, and another 575 years performing 
their courses in their respective orbits. 

191. The number of comets already observed 
is about five hundred ; one of which appeared 
in the year 1680, Sir Isaac Newton imagined to 
have been, when nearest the sun, 2000 times hot- 
ter than red-hot iron, and that if it were so large 
as the earth, it would take at least 50,000 years 
to cool, and its tail was 80 millions of miles in 
length. The splendid comet of 1 8 1 1 , when near- 
est the earth, was 114 millions of miles distant. 
It was about the size of the earth, and was visible 
during three or four months. Its tail was 11 mil- 
lions of miles long. The comet of 1819 had a 
very majestic appearance ; it was not visible here 
until it had passed its perihelion. Its tail was 
at least 15 millions of miles in length. 

OF THE FIXED STARS. 

192. The universe, so far as human observa- 
tion has extended, consists of infinite or bound- 
less space, iu which are numberless fixed stars, 
of the nature, bulk, and properties of the sun; but 
because they are at such immense distances from 
the earth, they appear to our eyes only as so ma- 
ny beautiful shining points. 

193. The fixed stars are bodies shining by 
their innate effulgence ; each is supposed to be 
the centre of a system, like our solar system, 



60 OF THE FIXED STARS, 

with primary and secondary planets, comets, Ac- 
revolving respectively around it. 

194. All the fixed stars, excepting the polar 
star, appear to have a motion like the sun and 
moon, rising in the east, increasing in altitude un- 
til they approach the meridian, and declining to 
the western horizon, where they disappear. 

195. The apparent motion of the stars from 
east to west, is occasioned by the revolution of 
the earth on its axis from west to east. 

196. The polar star is the only one which ap- 
pears stationary, both as it respects its position 
among the other stars,and also with regard to the 
earth. 

197. This immovable appearance of the po- 
lar star, is occasioned by the axis of the earth 
pointing directly to it. Its elevation above the 
horizon of any place, is always equal to the lati- 
tude of that place, or its nearest distance to the 
equinoctial. 

198. The stars appear innumerable on a clear 
winters evening. This is occasioned partly by 
viewing them all at the same time, and partly by 
their incessant twinkling. Not more than five 
hundred can be individually numbered on any 
evening with the naked eye. 

199. The distances of the fixed stars cannot be 
ascertained with any degree of certainty, beQ&usv 
the diameter of the earth's annual orbit, which is 
190 millions of miles, is a mere point when com- 
pared with their inconceivable distance. 

Ota. — Various methods have been adopted by the most 
eminent astronomers, to endeavour to ascertain the dis- 



TZ.7. 




'Ms 



OF THE FIXED STARS. 61 

tances of the fixed stars, but all have hitherto failed in 
producing any satisfactory conclusion. The diameter of 
the earth's annual orbit, which is 190 millions of miles, 
does not form an angle of %" at the nearest fixed star. 

200. The stars, when viewed through glasses 
of the greatest magnifying powers, appear the 
same size as without the telescope; while the 
planets are magnified in appearance, according to 
the power of the instrument with which they are 
viewed. 

Ob s , — The swiftest motion we know of, is light, which 
is about eight minutes coming from the sun to the earth, 
yet light would be a year and a quarter coming from Si- 
nus, the nearest fixed star, to the earth. A cannon ball, 
which moves at the rate of 20 miles in a minute, would 
fee 760,000 years in coming from Sirius to us, if it vyere to 
proceed with the same velocity as when first projected. 
Sound, which moves 1142 feet in a second, or about 13 
miles in a minute, would be upwards of a million years 
reaching us from the nearest fixed star ! 

201. For the purpose of more readily noticing 
auy particular star, astronomers have divided 
the stars into six sizes or magnitudes, each class- 
ed according to its brightness. 

202. For the purpose of finding and referring 
to any particular star, the Babylonian astrono- 
mers first divided the stars into asterisms or con- 
stellations, such as bears,lions, dogs, the horse,the 
bull, the ram, &c. just as they fancied any partic- 
ular cluster of stars to represent the predominant 
parts of any particular animal. 

Obs.— But modern astronomers have, with greater pre- 
cision, represented the stars in any particular constella- 
tion, by the letters of the Greek alphabet, according to 



62 OF THE FIXED STARS. 

their brightness, and thus have superseded the necessity 
of having these animals depicted on the celestial globe. 

203. The number of constellations is 93. There 
are 34 north of the zodiac, 12 zodiacal constella- 
tions, and 47 south of the zodiac. 

204. There are 20 stars of the largest size, 
called stars of the first magnitude ; 65 of the sec- 
ond ; 295 of the third ; 435 of the fourth ; 648 
of the fifth ; and about 1500 of the sixth magni- 
tude ; being all that can be seen with ttie naked 
eye, from all sides of the earth ; the others can 
only be seen with a telescope. 

205. The principal constellations are Orion, 
containing a sword and luminous belt; Sirius,the 
brightest of the stars, in Canis Minor> in the 
south ;in the north are Ursa Major,in which are 
seven very conspicuous stars, two of which are 
called the Pointers, because they always point di- 
rectly to the pole star, which is in Ursa Minor. 
Cassiopeia, representing a W,badly made, in the 
north. There are in the east Taurus, containing 
the Pleiades, and Aldebaran among the Hyades, 
all very conspicuous in our winter evenings. 

Obs. — The best way to distinguish any particular star, 
or cluster of stars, is with a celestial globe, byProb. 15; 
for, by rectifying the globe forany particular day, hour, 
and place, the star we observe in the heavens, whose 
name we wish to know, is in the exact position, altitude, 
&c. as in the firmament, and by its situation with respect 
to other stars, may very easily be named. 

206. The Milky Way is a light gleam of im- 
mensely distant and numerous stars extending 
from the northern to the southern side of the 



LIST OF THE CONSTELLATIONS. 



63 



heavens, and which are visible only by a teles- 
cope of great magnifying power. 

20 7o The firmament appears when viewed 
through a good telescope, abounding with num- 
berless stars, which are invisible to the naked 
eye, on account of their distance. In a small 
portion of the Milky May, the celebrated astron- 
omer Herschell says, he observed and counted 
1 1 6,000 stars in a quarter of an hour. 

A LIST OF THE CONSTELLATIONS. 



Zodiacial Constellations. 


Names of the Constellations. 


6 5 


4 

Principal Stafs. 






z;x 




Aries 


The Ram 


66 


Arietis 2 
C Aldebaran 


Taurus 


The Bull 


141 


<The Pleiades 
f The Hyades 


Gemini 


The Twins 


85 


^"Castor 1 
£ Pol lux 2 


Cancer 


The Crab 


83 




Leo 


The Lion 


95 


CRegulus, or 
\ Lion's Heart 


Virgo 


The Virgin 


110 


J SpieaVirginisl 
/ VendemiatrixS 


Libra 


The Balance 


51 




Scorpio 


The Scorpion 


44 


Antares 1 


Sagitarius 


The Archer 


69 




Capricornus 


The Goat 


51 




Aquarius 


The Water bearer 


108 


Scheat 3 


Pisces 


The Fishes 


113 





64 



LIST OF THE CONSTELLATIONS. 



The Northern Constellations, 



Names of the Constellations. 



fc"* 3 



h Wagoner 



Ursa ^inor 

Ursa Major 

Cassiopeia 

Perseus 

Auriga 

Bootes 

Draco 

Cepheus 

Canes 

nati 
Cor Caroli 
Triangulum 
Triangulum 

Minus 
Musca 
Lynx 
Leo Minor 
Coma Bere-? 

nicis. £ 

d 'dalus ar " | The Camelopard 
Mons Mene- 

laus ... 

Corona Bo- ") The Northern 

real is 3 Crown 
Serpens The Serpent 

bcutum So- > The Shield of 

bieski £ Sobieski 
Hercules cum ) 

Ramo et£ Hercules kneel 

Carbo ) ing 

He pnn^arius ) 



The Little Bear 

The Great Bear 

Lady in her Chair 

Perseus 

fl 

The Bear Driver 

The Dragon 

Te *> 
ici c T}ie Greyhounds 

Charles' Crown 
The Triangle 
The Lesser Trian- 
gle 
The Bee 

The Little Lion 
Berenice's Hair 



sive Ophiu- 
chus 



Serpent 



&4 
87 
55 
59 
66 
54 
80 
35 

25 

3 
16 



6 

44 

n 

40 

58 

11 

21 

50 

8 



Hi 



68 



Principal Stars. 



Pole Star 2 
Dubhe 1 
Schedar 3 
Algenib % 
Capella 1 
A returns 1 
Rastaben 3 
Alderamin 3 



Ras AlgiathaS 
Ras Alhagus 3 



LIST OF THE CONSXE&LATIONS. 



65 



The Northern Constellations (continued.) 



Names of the Constellations. 






Taurus Ponia 

toivski 
Vulpecula 

et Anser 
Lyra 
Sagitta 
Aquila 
Deiphinus 
Cygnus 
Equuleus 
Lacerta 
Pegasus 
Andromeda 



The Fox and 

Goose 
The Harp 
The Arrow 
The Eagle 
The Dolphin 
The Swan 
The little Horse 
The Lizard 
The Flying Horse 



7 

S7 

2£ 
18 
40 
18 
73 
10 
16 
85 
66 



Principal Stars 



Vegal 
Altair 2 
Deneb Adiga 1 



Markab 2 
Almaac 2 



Southern Constellations. 



Phoenix Phenix 

Officina Sculp- 1 The Sculptor's 

toris S Shop 

Eridanus The River 

Hydrus The Hvdra 

Cetus The Whale 

Fornax Cher- } ^i t? 

> I he Furnace, 
nica S 

Horologium The Clock 

Refcieulus ) The Rhomboi- 

Rhomboidalis $ dal Net 

Xiphias The Sword Fish 

Ccela Sculptoris, CThe Engra- 

or Praxiteles £ ver's Tool 

Lepus The Hare 

Columba Nao-" 



chi 



i 



Noah's Dove 



IS 

12 

76 
10 
80 

14 

12 

10 

7 

16 
19 

10 



Achernar 1 
Menkar 2 



6* 



66 



LIST OP THE CONSTELLATIONS. 



Southern Constellations (continued), 



Names of the Constellations. 



Orion - 

Argo Navis The Ship Argo 

Canis Major The iireat Dog 



Ijlquuleus 

Picionius 
Monoceros 
Canis Minor 
Chamaelon 



S The Painter's 

\ Easel 

The Unicorn 

The Little Dog 

Chameleon 
i The Mariner's 
\ Compass 



Pixis Nautica 

Piscis Volans The Flying Fish 
Hydra - 

Sextans The Sextant 

Machina Pneu- ^ The Air 

matica 
Crater 
Corvris 
Crux 
Musca 



Pump 

The Cup 

The Crow 

The Cross 

The Bee 
CThe Bird of Para 
£ dise 

The Compasses 

The Centaur 

The Wolf 



A pus 

Circinus 

Centaurus 

Lupus 

«.ua£aEu-$ Euc iid» B Square 

clidis £ * 

Triangulum J Southern Trian 

Australe ( gle 
\ra The Altar 

Telescopium The Telescope 
'orona Aus- ^ Southern 

trails ( Crown 

Pavo The Peacock 

Indus The Indian 



55£ 
73 ' 
50 
30 

8 

31 

14 
10 

4 

8 

60 

4 



31 
9 
6 

4 

11 



n 

12 



9 
9 

n 

14 
12 



Principal Stars. 



Betelgeuse 1 
Canopusl 
Sirius 1 



Procyon 1 



Cor. Hydras 1 



Alkes 3 
Algorab 3 
Crucii 1 



OF ECLIPSES. 



67 



Southern Constellations (continued J. 


Names of the Constellations. 


O v. 

O 8? 


Principal Stars. 


Microscopium 1 he Microscope 
Octans Bad- ^ Hadieys Q,uad- 

leinaus ( rant 
Grus The Crane 
Toucan American Goose 
Piscis Austra- $ The southern 

lis I Fish 


10 

45 

14 
9 

20 


Fomalhaut 1 



OF ECLIPSES- 

203. An eclipse of any celestial body is an 
obscuration of its light, occasioned by one body 
passing through the shadow of another celestial 
body. 



Obsr 1.-— Those phenomena termed Eclipses,were for- 
merly beheld by mankind with terror and amazement, 
and looked upon as prodigies which portended calamity 
and misery; these fears, and the erroneous opinions that 
produced them, had their source in the hieroglyphicai 
language of the earth. The vulgar, in all ages, have 
beheld eclipses with a kind of terror : not having been 
able to account for the obscuration of any of the celes- 
tial bodies, superstition has invented a thousand ridicu- 
lous stories to account for this seeming wonderful phe- 
nomenon, 

2. The natives of Mexico keep fasts during eclipses, 
imagining the moon has been wounded by the sun in a 
quarrel. Other nations have thought, that in an eclipse 
of the sun, that body has turned away his face with ab- 
horrence from the crimes of mankind ; and, by fasting, 
they think to appease his wrath. 

5. This ignorance of mankind was essentially useful to 



68 OF ECLIPSES. 

that great navigator Columbus. In the year 150£, this 
most enterprising navigator undertook his fourth vo\age 
of discoveries. When he arrived at St. Domingo, he had 
the mortification to find the Spanish governor, who resi- 
ded there, would not allow his ships to anchor, because 
he was jealous of the favours which Columbus had receiv- 
ed from Isabella, then Queen of Spain. This obliged 
liim to put to sea in search of some more hospitable har- 
bour. After he had searched in vain for a passage to the 
Indian Ocean, he returned, and was shipwrecked on the 
coast of Jamaica. Being driven to great distress, in con- 
sequence of the natives withholding a supply of provis- 
ions, he had recourse to a happy artifice, which not on- 
ly produced the desired success, but heightened the fav- 
ourable ideas the Indians had originally entertained of 
the Spaniards. By his skill in astronomy he knew there 
would shoitly be an eclipse of the moon. He assembled 
all the principal persons of the district the day before 
the eclipse happened; he then severely reproached them 
for their caprice, in withholding their assistance from 
men whom they had so lately and so highly respected; and 
told them that the Great Spirit was so offended at their 
want of humanity to the Spaniards, His faithful ser- 
vants, that, as a sign that He intended to punish them 
with extreme severity, ' that very night the moon should 
withhold her light, and appear of a bloody hue, as a 
sign of Divine wrath, and an emblem of His vengeance 
ready to fall on them. Some of them heard this threat 
with indifference, and others with astonishment ; but 
when the moon began gradually to be darkened, all were 
struck with terror. They ran with consternation to their 
houses,and returned instantly loaded with provisions. 

209. Every dark body upon which a light one 
shines, will evidently cast a shadow in a position 
opposite to that light : and every dark globular 
body, upon which a larger one shines, will cast a 
conical shadow. (Yide Fig. 1. Plate VIL) 

210. Eclipses are of two sorts, viz. of the sun, 
and of a secondary planet, as the moon, the satel- 
lites of Jupiter, &c. 



ECLIPSES OF THE SUN. 69 



Eclipses of the Sun. 

211. An eclipse of the sun is occasioned by the 
earth's passing through the shadow of the moon, 
when the rays of the sun are intercepted by the 
naoon's body, and so prevented from reaching the 
earth. 

212. As the moon must be in a line between 
the earth and the sun, to intercept his rays from 
us, eclipses of the sun must always happen at the 
time of new moon, or when the moon is in con- 
junction with the sun. 

Obs. — This is a proof that the darkness recorded in the 
Scriptures, at the time of our Saviour's crucifixion was 
supernatural, and not caused by an eclipse of the sun; 
for the passover was always held at full moon according 
te the Jewish law : it is therefore evident that she was 
not in a position to darken that luminary. 

213. As the earth and sun are in the plane of 
the ecliptic, the moon's shadow must be in that 
plane either to eclipse the sun or to be eclipsed 
herself. The moon must, therefore, be in one of 
her nodes to eclipse the sun or to be eclipsed. 

Ob. 1. — By knowing the place in the ecliptic of the 
moon's nodes, we may very readily ascertain when to 
expect a solar or lunar eclipse. The solar eclipse 
happening at the conjunction, and the lunar eclipse at 
the opposition, nearest to the moon's nodes. 

2. The sun being a lucid body, be is not deprived of 
any of his light during the time we call a solar eclipse. 
The apparent dark portion of his surface is the moon's 
passing across his disc, or rather the earth's parsing 
through the moon's shadow; and,as the dark hemisphere 
of the moon is toward us, she is invisible. An eclipse 
of the sun is, properly speaking, an eclipse of the earth. 



70 ECLIPSES OF THE MOON. 

21 4. As ilie moon moves round the earth from 
west to east, the western side of the sun will be 
first eclipsed ; then the centre, and the eastern 
side last. 

Obs. — (Plate Til. Fig. 2.) I^et S represent the sun, 
M the moon, and E the earth ; c a b d a portion of the 
conical shadow of the moon : a b the portion thereof 
which touches the earth, E ; this portion of the moon's 
shadow is called the umbra, and this umbra never ex- 
tends over a greater portion of the earth's surface than. 
180 miles; to all which portion of the earth the son will 
be totally eclipsed, because the sun will be hidden en- 
tirely by the body of the moon. The portion of the 
shadow c a e,d bf, is called the penumbra, which may 
cover a space of 4900 miles,and the portions of the earth 
a e, bf, will see the sun partially eclipsed. Upon every 
portion of the earth where the penumbra does not fall, 
and where the sun is visible, he will not appear eclipsed 
at all. 

215. An eclipse of the sun does not happen to 
all places at the same time, but appears earlier or 
later as the place is situated to the westward or 
the eastward ; the motion of the moon being in 
that direction. 

Eclipses of the Moon. 

216. An eclipse of the moon is occasioned by 
her passing through the conical shadow oi the 
earth, which shadow being dark, obscures her 
surface, and she is then deprived from receiving 
the light of the sun ; just as if (vide Fig. 3. Plate 
VII.) S, E, and M represent the sun, earth, and 
moon ; M is eclipsed when passing through the 
shadow of E. 

Obs. — An eclipse of the moon with us is an eclipse of 
the sun to the inhabitants of the moon; because the por- 



ECLIPSES OF THE MOQN, <1 

tion of the moon which appears dark to us during; an e- 
clipse, is actually deprived of the light of the sun. by the 
interposition of the earth ; therefore the inhabitants of 
the eclipsed portion of the moon are prevented from see- 
ing a portion of the sun; he therefore appears eclipsed to 
them. 

217. An eclipse of the moon must happen when 
she is in opposition to the sun, that is, always at 
a full moon, which foil moon happens nearest to 
the time that she is in her nodes, 

218. As the moon is actually deprived of the 
rays of the sun, during the time she is eclipsed, 
that eclipse is visible to every inhabitant of the 
earth who beholds the moon. 

219. The duration of an eclipse of the moon 
cannot exceed five hours and a half; and she can- 
not be totally eclipsed for a longer period than 
one hour and three quarters. 

220. If the moon moved in the plane of the 
ecliptic, there would be an eclipse of the sun at 
every conjunction, and an eclipse of the moon at 
every opposition of these bodies. 

Obs. — The nearest distance of the moon to the plane 
of the ecliptic is called her latitude ; and if her latitude 
at her opposition be greater than the sum of the semi- 
diameters of the moon and sun, she cannot be eclipsed ; 
but if her latitude be less than the sum of their semi-di- 
ameters, there will be a lunar eclipse. To illustrate this, 
(Plate VIII. Fig. 1.) Let GE be a portion of the eclip- 
tic, or orbit of the earth, and HF a portion of the moon's 
orbit; V. the place of the moon's node. If the moon be 
at V, when she is in opposition, she will be totally eclip- 
sed ; if at M. much eclipsed; when at O, less; and when 
at P, not at all; that is, when the sum of the semi-diam- 
eters of the sun and moon is equal to, or greater than 
the moon's latitude, which is, when the moon is about 
17° from her node: this distance is called the lunar eclip- 
tic limit; and when she is within 12° of her node* at the 



72 ECLIPSES OF THE MOON. 

time of conjunction there will be a solar eclipse. 
This is the solar ecliptic limit; and, consequently, the 
eclipses of the sun to the moon will be as 12 : 17,or near- 
ly as 2 to 3. 

221. When the centres of the earth, the sun, 
and moon, are in an imaginary right line, the e- 
clipse is called centra); when the whole disc of 
either of the celestial bodies is obscured, the 
eclipse is called total; when a part of either lumi- 
nary is obscured, the eclipse is called partial ; 
and when, in solar eclipses, the moon appears in 
the middle of the sun, and the sun seems to form 
a ring round the moon, the eclipse is called an- 
nular. 

222. Eclipses of the sun are more frequent 
than those of the moon ; and yet there are,to any 
particular place, more visible eclipses of the 
moon than of the sun ; because every eclipse of 
the moon is visible where she is visible, but an 
eclipse of the sun is only visible to a small por- 
tion of the earth even when the sun is visible. 

223. The greatest number of eclipses that can 
happen in a year are seven, and the least number 
two ; and these two must be both of the sun; the 
general number is four; two of each luminary. 

224. The diameters of the sun and moon are 
supposed to be divided into twelve parts, called 
digits, and as many of these parts as are obscured 
in an eclipse,so many digits the body is said to be 
eclipsed. 

Obs. h — A. solar eclipse may be partial, central, total, 
and annular, at d liferent places on the earth at the same 
time. 

2. The lunar eclipses, by appearing to all places on 
the earth at the same time, are very useful in determin- 
ing the difference of longitudes of places. If the eclipse 



TABLE OF ECLIPSES. 



13 



be observed at two places with great exactness, by a 
well regulated time-piece, the difference in the times of 
observation, reduced into degrees, by allowing 15° to an 
hour, will give the difference of longitude of those pla- 
es. 

225. The moon's nodes are not always in the 
same sign and degree of the ecliptic, but have a 
retrograde motion of about 19° every year,which 
causes eclipses to happen irregularly, as they de- 
pend on the motion of the moon's nodes. 

Obs. 1. — The exact time which the moon's nodes take 
to revolve from any particular part of the ecliptic to 
their being there again, is 18 ys. 11 ds. 7 hs. 43 min.20 
sec. when there are only four leap-years in these 18 
years; but when there are five leap-years in these 18 
years, then the exact period is 18 ys. 10 ds. 7 hs. 43 min. 
20 sec. This period is called the Chaldean Saros. 

2. This affords us at once a very sure and easy method 
of calculating eclipses for any future period; for, by no- 
ticing from any table of conjunctions, or from any alma- 
nac, the exact time of conjunction of the sun and moon, 
by adding the Chaldean saros to that time, we have the 
period when the same eclipse will return again. 

A Table of Eclipses, (from Keith.) 



182i 



1824 



1825 



DP 



Months 

and 
Days. 



Tuly 8 
July 23 
Jan. 16 
June 26 
July 11 
Dec. 20 
P 1 June 1 



Time. 



6J M 

3JM 
9 M 

114 a 

44 M 
11 M 

04 M 



1825 



1826 



1827 



DP 
F 
DT 

m 
m 

DP 



Months 
and 
Days. 



June 16 
Nov. 25 
May 21 
Nov. 14 
Nov. 29 
4pril 26 
May 11 



Time. 



04 A 
44 A 
24 A 
44 A 
114 M 
34 M 
8J M 



74 



TABLE OF ECLIPSES. 



1827 
1828 

1829 



1850 



1851 



18:32 

1853 



1834 
1835 



1836 



1837 



1838 
1839 
1840 



J)P 

© 

D? 



DT 

JP 
DP 

© 

DP 

DP 

© 

])r 
jr 
DP 

DP 

© 

DP 

®„ 
D p 

D r 

/;"? 
fsi 

DT 

21 

DP 

© 

© 

DP 

© 

DP 



Monttis 
and 
Days. 



Nov. 3 
Vpril 14 

Oct 9 
March 20 
Sep. 13 
Sep. 28 
Feb 23 
March 9 
Sep. 2 
Feb. 26 

Aug. 23 
July 27 
Jan. 6 
July 2 
Ju!y 17 
Dec. 26 
June 21 
E>ec. 16 
May 27 
June 10 
Nov. 20 
VI ay 1 
May 15 
Oct. 24 
April 20 
May 4 
Oct. 13 
April 10 
Oct 3 
Ma,chl5 
Sep. 7 
Feb. 17 
Marsh 4 
Aug. 13 



Time. 



5 

H 
0i 
2 
7 

2* 

5 

2 
11 

t . 

lOi 

24 

8 

1 

7 
10 

84 
5* 

li 
11 

it 

H 

9 

m 

2* 

3 

2| 

2 
4 

n 



A 
M 
M 

A 

M. 

l\I 

M 
A 
A 
\ 

M 
A 
M 
M 
M 
A 

M 
fit 

A 
A 
M 
M 
A 
A 
A 
A 
A 
M 
A 
A 
A 
A 
M 
M 



1841 



184^ 



1843 



lo44 



lb 45 



1846 



1847 



1848 



1849 



yr 



DP 

© 

Dp 

Dp 

Dp 
© 
Dl 
DT 

© 

DT 
DP 

© 

© 
2>P 

© 
© 
5t 
Dt 



dp 
Dp 



1850 



1851 



1852 



Months 

and 

Days. 



DP 

DP 
© 
DT 
DT 

a 



Feb. 6 
Feb. 21 
July 18 
Aug. 2 
Jan. 26 
July 8 

July 22 
June 12 
Dec. 7 
Dec. 21 
May 31 
Nov. 25 
Mav 6 
May 21 
Nov. 14 
April 25 
Oct 20 
March 3 1 
Sep. 24 
Oct. 9 
March 19 
Sep. 13 
Sep. 27 

Feb. 23 
March 9 
Sep. 2 
Feb. 12 
Aug. 7 
Jan. 17 
July 13 
July 28 
Jan. 7 
July 1 
Dec. 11 



Time. 



2| 
11 

2 

10 

6 

7 

11 

8 

04 
54 

ni 

oi 

10J 

44 

l 

5J 

3£ 
94 

3 

n 

H 
64 

10 

14 
l 

54 

64 

10 
5 

H 

H 



M 
M 
A 
M 
A 
M 

M 
'M 
M 
M 
A 
M 
M 
A 
M 
A 
M 
A 
A' 
M 
A 
M 
M 

M 
M 
A 
M 
A 
A 
M 
A 
M 
A 
M 



ASPECTS OF THE PLANETS.. 75 



OF THE ASPECTS OF THE PLANETS. 

226. The aspects of the planets contributed ia 
the early ages of astronomy, to form the true 
or Copernican system, upon the ruins of the false 
systems which astronomers first invented. 

227. The aspects of the planets are five, viz. 
conjunction, marked thus 6 ; opposition, thus § ; 
quartile. thus □ ; sextile, thus ^ ; and trine, 
thus A- The ascending node of a planet is mark- 
ed Q, and the descending node y. 

228. When two planets, or any two celestial 
bodies are in the same portion of the zodiac as 
seen from the earth, that is, when their geocen- 
tric longitudes are the same, they are in con- 
junction. 

229. Conjunctions are of two sorts, inferior and 
superior. 

230. An inferior conjunction is when an infer- 
ior planet is directly between the earth and the 
sun ; and a superior conjunction is when the sun 
is between the earth and the planet 

231- When any planet or celestial body is in 
opposition to the sun, such planet is in the same 
sign and degree in the ecliptic as the earth is, 
and is on the meridian at midnight, or twelve 
o'clock at night. 

Ohs. 1. — The earth's place in the ecliptic is always six 
signs.or 130 distant from the sun's place; and any plan- 
et being in opposition to the sun, has its place 180° or 
six signs from the sun's place. 

2. The diagram (Plate VIII. Fig. 2.) will very readi- 
ly illustrate the inferior and superior conjunctions of 



76 ASPECTS OP THE PLANETS. 

the inferior planets, with the conjunctions and opposi- 
tions of the superior. 

Let V V V" represent the orbit of an inferior plan- 
ers Venus; £ E' E" the orbit of the Earth, M iVT M" 
the orbit of any superior planet, as Mars let S repre- 
sent the sun in the centre. Now Venus, the Earth, and 
Mars all appear, when at V, E, and M, in the same po- 
sition of the zodiac when viewed from the sun ; namely 8 
in =2a ; their heliocentric places are the same ; but Ven- 
us, when at V, appears to a spectator on E to be in °p: 
this position of Venus is denominated her inferior con- 
junction,she being then immediately between S,the Sun, 
and E, the Earth ; and the point of the ecliptic, ^ i& 
her ireocentric place; consequently her geocentric place 
is six sitz;ns distant from her real or heliocentric place. 
When Venus, is at V" she is then in her superior con- 
junction, it is evident that the planet Venus is never 
visible to us at her inferior or superior conjunction* 
She, at her inferior conjunction, will sometimes appear 
to cross the sun's disc, and is then seen like a spot on 
his surface. This transit may continue five hours. The 
planet Mars, when at M, is in the same poiut of the e- 
clipticas the earth is, and is then in opposition to the 
sun. He comes to the meridian then at midnight. 

232. The inferior planets have an inferior and 
a superior conjunction, but no opposition ; and 
the superior planets have an opposition and a 
conjunction, but no inferior conjunction. Any 
planet being in opposition to the sun, is in the 
same sign as the earth is, or six signs from the 
sun's place. 

Obs. — By considering that no inferior planet can be 
seen in the night, we have an infallible criterion to tell 
at first sight the name of any planet we may observe 
in the evening If it be of a red fiery appearance, it is 
Mars; if a lustre far surpassing even the brilliancy of Si- 
rius it is Jupiter; but if it be noticed as a star of the 
second magnitude, moving very tardily around the cen- 
tre of the system, it is Saturn, the most distant of the 
planets observable to the naked eye. 



ASPECTS OF THE PLANETS, tl 

233. When any planet has a quartile aspect 
with respect to another celestial body, its geocen- 
tric place is then three signs, or 90° from the geo 
centric place of that celestial body. 

234 When any planet has a sextile aspect 
with respect to auother celestial body, its geocen- 
tric place is two signs, or 60° distant from that 
celestial body. 

235. When one heavenly body has a trine as- 
pect with regard to another celestial body, their 
geocentric places are four signs distant, that is, 
120°. 

236. These aspects of the planets, and of the 
other celestial bodies, were considered ot very 
great moment in astrological calculations. The 
planets situated according to auy of these aspects, 
being imagined by astrologers to have various 
influences on the destinies of mankind. 

Of the real and apparent Motions of the Planets^ 
and the Determination of the Distances of the 
inferior Planets. 

237 . All the planets move in one direction a- 
round the sun, as a centre, going through the 
twelve signs of the zodiac, in grand majectic suc- 
cession, from west to east. 

238. This revolution of the planets, from Aries, 
through Taurus, Gemini, &c. is their real, gen- 
erally called their direct motion; and whatever 
sign of the zodiac they may be in, as seen from 
the sun, is their real place. 

239. The apparent place of any celestial bo- 
dy, is its situation in the zodiac, as seen from 
the earth, so that heliocentric is synonymous to 
real; and geocentric, to apparent. 

: 7^ 



73 ASPECTS OF THE PLANETS. 

240* The planets frequently appear to us to 
move backwards, or contrary to the order of the 
signs; this backward motion is called their re- 
trograde motion, or motion antecedentia. 

241. The retrograde motion of an inferior 
planet is occasioned by its motion through the 
zodiac being quicker than the motion of the earth 
in the ecliptic ; and the retrograde motion of a 
superior planet is occasioned by the earth's mo- 
tion being quicker than the motion of such su- 
perior planet in its orbit; the stationary appear- 
ance of a planet is occasioned by such planet 
having a quicker or slower motion in its orbit, 
than the earth has in the ecliptic. 

Obs. 1.— (Plate VIII. Fig. S.) Let E represent the 
earth, V the position of the planet Venus, when inner 
inferior conjunction V 1 , V a , V3, V4, and VS, vartaus 
positions of the planet while revolving around S. When 
Venus is at V, her inferior, and V3,her superior conjunc- 
tion, she will appear to a spectator at E to be in «y> ; 
when she is in that part of her orbit represented by Vs t 
she will appear at d, and when she is at V 1 at a. When 
Venus is moving from V5 to V x ,she will, to a person sta- 
tioned at E, appear to describe the arc d c op X ff 5 
and, while moving from V 1 to V>, she will appear to 
recede, and describe the arc a b op & d. This is called 
her direct, and that her retrograde motion. When she 
is at V 1 or VS, she will appear to remain at a and d some 
time. This is called her stationary appearance. But 
by reason of tlie planets' proximity to the sun, she is in- 
visible to the eye of a spectator at E, excepting at V 1 
or V 1 , when she appears westward of the sun, and illu- 
minates our horizon just before the sun has begun his 
daily course, and she is then denominated the Morning 
Star; or, when she is atV4orVs, and is eastward of 
the sun, she then rises after the sun, and sets after him. 
She then adorns the western sky in the evening, and is 
denominated the Evening Star. 



SUPERIOR PLANETS. 79 

% By noticing the same figure, we observe that the 
inferior planets never are very distant from the sun's 
place. The distance of an inferior planet's geocentric 
place and the sun's place is the planet's elongation, e- 
qual to the angle formed at the earth by imaginary lines 
from the sun and planet, equal to the angle f Ea, this 
is called the planet's greatest elongation. This, in the 
planet Venus, is 48° 

3. From the greatest elongation of an inferior planet, 
we derive an easy method of finding its distance from the 
sun. For let V 1 and S be joined then in the right angled 
triangle E V 1 S right angled at V 1 , we have E S=95 
millions of miles, and the /V l ES=48°, to find V> 8 • 
that is, as Rad=S / /V I : E S=95 : : S^E=48° : V« 
S=the planet's distance from the sun. 

Of the direct and retrograde motion of the Su- 
perior Planets, the Determination of their 
Distances. &c. 

Let S (Plate VIII. Fig. 4.) represent the sun, 
eEe v the orbit of the earth, M any position of 
either of the superior planets, as Mars. JNow let 
us imagine the planet M to be stationary, while 
the earth moves through the arc eEe\ The plan- 
et M to a spectator at E appears at <y>; at e\ M 
appears at a ; and at e, M appears at b. When 
the earth is moving through the arc eEe\ the plan- 
et will appear to go through the arc b^a, or to 
move retrograde. When the earth is at e\ the 
planet will appear stationary ; and when the earth 
is moving from e\ onward in her orbit, the plan- 
et's motion will be direct. 

This diagram affords us an easy method of 
finding the distance of any superior planet ; for 
by joining eS 5 in the right angled triangle M e S, 
we have eS~Q5 millions of miles ; and the ob» 



80 ON PARALLAX, 

served ZeM S, to find SM, the planet's mean dis- 
tance from the sun : or the same distance may be 
found with the planet's horizontal parallax. 

242. The retrograde motion of an inferior 
planet happens when that planet is at its greatest 
elongation, and the retrograde motion of a supe- 
rior planet just before its opposition to the sun. 

ON PARALLAX. 

243. The parallax of any celestial body is the 
angle the semi-diameter of the earth forms at that 
body. 

(Plate ViT. Fig. 4.) Let SCD represent the 
diameter of the earth, C its centre, P any celes- 
tial body viewed by a spectator at S ; then is the 
angle SPC, the parallax of the body P, equal to 
the angle b Pa, equal to the angle the radius SC 
of the earth forms at the body P. 

244. The place in which any celestial body 
would appear, to a spectator at the earth's cen- 
tre, is called its true place; and the place where 
it actually does appear, its apparent place. 

Obs. — The parallax of any celestial body added to its 
apparent place will give its true place. 

245. The parallax of any body, when in the 
horizon, is called its horizontal parallax. 

Obs. — By knowing the horizontal parallax of any ce- 
lestial body, we can very readily find its distance from 
us by plane trigonometry. 

246. The angle which the sun and earth form 
at any planet or star, is called the parallax of the 
earth's annual orbit. 



-PZ.8. 





ABSTRACT OF ASTRONOMY. 81 

Obs. — The farther distant any celestial body is from 
us, the less will be its parallax. Thus the parallax of 
the moon is 57' 48" ; of Mars 23.6" ; of the sun U.7 f ; 
and the fixed stars are so distant that they have scarcely 
any parallax with the earth's annual orbit. 



ABSTRACT OF ASTRONOMY. 

The solar system comprises the sun, and all 
bodies which revolve around him as a centre. 
These are planets, comets, and asteroids. 

The number of comets is unknown. About 
five hundred have already been observed. 

There are seven primary planets,and eighteen 
secondary planets. 

The figure of the earth is not that of a perfect 
globe, the equatorial diameter being a little long- 
er than the polar. 

The planets Jupiter and Saturn are also obser- 
ved to be flattened at the poles, but in a greater 
proportion than the earth This is caused by the 
revolutions of those planets on their axis, and 
these axis being inclined always in one direc- 
tion. 

The orbits of all the planets, asteroids, comets, 
and satellites, are elliptical, having the sun or 
planet around which they revolve in one of the 
foci of the elliptic curve. 

The periods, distances, and magnitudes of the 
planets have all been determined with very con- 



82 ABSTRACT OF ASTRONOMY 

siderable exactness, but the orbits of the comets, 
being so very eccentric, these bodies only appear- 
ing when in their perihelion, or nearest distance 
to the sun, their theories are consequently merely 
hypothetical. 

The planets, comets, and satellites are preserv- 
ed iu their orbits by the power of gravitation. 
This was first proved by Sir Isaac JNewton. 

Ail the planets revolve about an imaginary 
line within themselves, called their axis. The 
time in which a planet revolves around its axis is 
called its day. The time a planet takes to re- 
volve around the sun forms its year. 

The different lengths of the day and night are 
occasioned by the inclination of the axis of the 
earth. 

The different seasons are occasioned by the 
different lengths of day and night. 

Jupiter is the largest planet in the solar sys- 
tem ; and yet it takes the least time to revolve on 
its axis. 

Mercury is the least planet in the solar system ; 
and yet it takes nearly the longest period to re- 
volve on its axis. 

The moon's year consists only of twelve days, 
and each of her days is 29i- of our days in length. 

The moon is the only body we know of which 
revolves on its axis from east to west ; all other 
bodies revolving from west to east. 

The fixed stars are distinguished from the 
planets by their twinkling, and by their being 
always in one position with respect to each 
other. 

The stars have no sensible magnitude, even 



. ABSTRACT OF ASTRONOMY. 83 

through the best telescopes, while the planets are 
increased m apparent magnituae,according to the 
magnifying powers of the instrument. 

The naked eye cannot discover more than five 
hundred stars on any clear evening; yet the fir- 
mament is supposed to contain eighty millions. 

Every star is supposed to be a sun, having 
planets, comets, &c. revolving around it. 

An eclipse of the moon is occasioned by her 

passing through the corneal shadow of the earth. 

An eclipse of the sun is occasioned by the 

earth's^ being io the conical shadow of the moon. 

Motion is the measure of time ; and the motion 
of the heavenly bodies is the basis by which all 
other motions are compared. 

The day is the first and grand division of time- 
all other portions being fouuded on this. 



84 



THE 



Elements of Astronomy. 



PART II. 



PLANETARY PROBLEMS. 

The following problems are founded upon the hypoth- 
esis, that the planets revolve around the sun in circular 
orbits, which though not mathematically correct, as has 
been proved in a preceding part of the work,is sufficient- 
ly so, to enable the young student to determine the so- 
lution of any question found herein with a correctness 
sufficiently exact for practical purposes. The demonstra- 
tions and the investigations of the following rules have 
been purposely omitted as their introduction would 
have been foreign to the design of the present work. 
The teacher is particularly recommended to enforce the 
stud\ of the subsequent problems, as they afford a test 
of arithmetical knowledge, and have a tendency to ma- 
ture the judgment and to ripen the understanding of the 
student, for the further prosecution of astronomical in- 
vestigations. 



PROBLEM I. 

To convert time into degrees, minutes, &c. &c. 

Rule. — Reduce the minutes, seconds, &c. into j 
decimal parts of an hour; then say, as 1 hour : 15° 
: : the time given : the degrees required. 



PLANETARY PROBLEMS. 8£ 

As 1 hr. : 15° : : 31 hrs. : 52i°=52 30'. 

2. How many degrees, &c. are equal to 4hrs, 
16 miri.? 

3. How many degrees, &c. are equal to 5hvs P 
11' 20"? 

4. loll hrs. 28' 1 8", how many degrees ? 

5. An eclipse of the moon was observed to 
commence at Greenwich at 1 1 hrs. 58' 53", and 
at New-York at 7hrs. 2' 50", what is the differ- 
ence of longitude of these two places. 

6. How many degrees is the Sun distant from 
the meridian at 4 hrs. 1 7' A. M. ? 

7. How many degrees is the Sun distant from 
the meridian, at lOhrs. 17' A. M.? 

8. If Saturn be in 7° of cf , in what degree of 
the ecliptic is Jupiter when this is on the merid- 
ian 2 hrs. 18' 19" after that? 

9. Saturn was observed to appear on the meri- 
dian, 40 minutes after Jupiter, how far were 
these planets asunder ? 

10. What is the difference of longitude of two 
places, to one of which the Sun appears on the 
meridian, 1 hr. 19' before he appears on the me« 
jidian of the other ? 

11. Two stars are observed to come on the 
meridian within 2 hrs. 49' 17 w ofeach other,what 
is their difference of longitude ? 

12. If Venus be observed to rise If hr. before 
the Sun, what is her elongation at that time ? 

13. If Jupiter set 3 hrs. 19' after the Sun, 
what is their difference of longitude ? 

14. On November 21, 1823, Saturn rises at 
6 hrs. 25' in,the moruing,and the Sun at 7hTS, 9* ? 
what is their difference of lougitude ? 

8 



86 PLANETARY PROBLEMS. 

15. On August 1, 1823, Venus sets at 9 hrs.3' 5 
in the evening, and the Sun at 7 hrs. 8', what is 
the elongation of Venus on that day ? 

PROBLEM II. 

To convert Degrees, Minutes ^ &c. into Time* 

Rule. — Reduce the minutes, &c. into deci- 
mal parts of a degree; and then say as 15° : lhr. ; ; 
the degrees given : the time required. 

EXAMPLES. 

16. What is the time answering to 84° ? 
Solution— As 15° : 1 hr. : : 84° : 5 hrs._3ef, 

the time required. 

17. What is the time answering to 78° 16' ? 

18. What is the time answering to 81° 17' ? 

19. What is the time answering to 123° 18' ? 

20. What is the time answering to 180° ? 

21 The difference of longitude of two places 
is 78° 10'; what is their difference in time l} 

22. The longitude of New-York is about 3° 
east of Washington; when it is 12 o'clock a*< 
Washington, what is the time at New-York ? 

23. The longitude of Amsterdam is 10°25'E. 
When it is 12 o'clock at Amsterdam, what is the 
time at London ? 

24. Dumfries is in 3° 23' W. ; Kingston in 76° 
37' W. What is their difference of time; and 
when it is 7 o'clock at Dumfries, what is the time 
at Kingston ? 

25. In an eclipse of the moon, the beginning 
will ue at 8 hrs. 18' at Philadelphia, when may 



PLANETARY PROBLEMS. S7 

it be expected at Boston, New-Haven, jN"ew- 
York,Charleston,S. C. Washington, and St, Lou- 
is ? 

26. If the greatest elongation of Mercury be 
28° 20', ■ how long can he rise before the Sun, 
when a morning star ? 

27. If the greatest elongation of Venus be 48°; 
how long does she rise or set before the suq, 
when she is in that portioo ot her orbit ? 

28. October 1, 1823. At this time Venus is in 
Libra, 22° 2'; Mars in Leo, 15° 33', Jupiter in 
Cancer, 9° 48'. What time elapses between these 
planets coming to the meridian ? 

29. The difference of longitude of two stars is 
73° 19' : how long will one be on the meridian 
before the other ? 

30. The difference of longitude of Jupiter and 
Mars on a certain day, is 3 sigus 7° 18' : what 
time elapses between these planets coming to any 
meridian ? 

31. The longitude of Venus 43° 1 7' ; and of 
Mars 93° 10' : how many hours elapse between 
these planets passing the meridian ? 

PROBLEM III. 

Having the Diurnal arc of the Sun, or of any 
Planet given, to Jind at what Hour the Sun 
rises and sets. 

Rule. — Bring the diurnal arc into time, by 
the last problem; divide the time thus found by 
2, and it will give the time the Sun sets ; if this 
time be taken from 12 hours, it will leave the 
time the Sun rises. 



8$ PLANETARY PROBLEMS 

EXAMPLES. 

32. The Sun's diurnal arc is 176° : at what 
fiour does he rise and set ? 
Solution.— As 15° : 1 hr : : 176°: 11 hrs. 44'. 
11 hrs. 44' 

Then =5 hrs. 52' = time the Sun 

2 
sets, and 12 h.—5 hrs. 52—6 hrs. 8'=the time 
he rises, 

33. The Sun's diurnal arc is 21 7° on a certain 
day; at what hour does he rise and set ? 

34. The Sun's diurnal arc is 170° 18' ; at 
what hour does he rise and set ? 

35. The Sun's diurnal arc is 151° 17'; at 
what hour does he rise and set ? 

36. The Sun's diurnal arc is 73° 12' ; at what 
hour does he rise and set ? 

37. The diurnal arc of Venus is 94° 17' ; at 
what hour does the Sun rise and set ? 

38. The diurnal arc of Mars is 196° 18'; at 
what hour does the Sun rise and set ? 

39 The diurnal arc of Jupiter is 213° 17'; 
at what hour does the Sun rise and set ? 

40. The diurnal arc of Saturn, is 200° 12' ; 
at what hour does the Sun rise and set ? 

4L When Venus rises at 5 o'clock, A. M.how 
many hours is she above the horizon ? 



PLANETARY PROBLEMS. 89 

PROBLEM IV. 

By having the Number of Hours the Sun,or any 
Planet is above the horisonfo find the Length 
of its diurnal or nocturnal Arc. 

Rule. — Divide the number of hours the Sun 
or plaoet is above the horizon by 2, and it will 
give the time the sun sets ; and if this be taken 
from 12 hrs. it will leave the time the Sun rises. 

The number of hours the Sun is f>bove the hori- 
zon, multiplied by 15°, will give the length of the 
Sun or planet's diurnal arc. 

EXAMPLES. 

42- When the Sun continues above the hori- 
zon 12 hours, at what hour does he rise and set, 
and what is the length of his diurnal arc ? 
12 

Solution, =6 hrs.=time the Sun rises 

2 
and sets, and 6 X ^°=?90°=the length of his di- 
urnal arc. 

43. When the Sun continues above the horizon 
13 hrs. 17\ at what hour does he rise and set, 
and what is the length of his nocturnal arc ? 

44. When Saturn continues 15 hrs. above the 
horizon, at what hour does the Sun rise and set, 
and what is the length of Saturn's nocturnal arc ? 

45. When Jupiter continues 17 hrs. 19' 24" a- 
bove the horizon, at what hour does the Sun rise? 

46. When Mars continues 20 hrs. 1 & 7" above 
the horizon, at what hour does the Sun set ? 



%* 



90 PLANETARY PROBLEMS. 

47. When Venus continues 13 hours, 14' 16" 
above the horizon,at what hour does the Sun set? 

48. On April 16, the Sun rose at 5 hrs. 17' ; 
how many hours from sun-rise to suu-set, and 
what is the length of his nocturnal arc ? 

49, On June 21, the Sun rose at 3 hrs. 47' ; 
how many hours from sun-rise to sun-set, and 
•what is the length of his diurnal arc? 

PROBLEM V. 

To determine the Number of Days which elapse 
between two Conjunctions or two Oppositions ; 
or between a Conjunction and an Opposition, 
of any two Planets. 

Rules. 1. — Find the difference of their daily 
motions, from the table on page 91. 

2. For 2 conjunctions, or two oppositions, say, 
as the difference of their daily motions: 1 day : : 
360° : to the difference in the times of two con- 
junctions required. 

3 For a conjunction and an opposition, or for 
an inferior and superior conjunction, say : as the 
difference of their daily motions : 1 day : : 
180° : to the time elapsing between a conjunction 
&nd an opposition of the two given planets. 



PLANETARY PROBLEMS, 



91 



Planets. 


Planet's Daily 
motion. 


Heli. Long. Jan. 
1. 1823. 


Mercury 

Venus 

Earth 

Mars 
Jupiter 
Saturn 
Herschell 


4.0928° 
1.6021 
.9856 
.5240 
.0831 
.0335 
•0118 


277° 25' 
285° 16' 
100° 20' 
311° 41' 
64° 51' 
38° 56' 
277° 30' 


Sun's Geo. Lo 


ngitude, Jan. 1 . 


280° 21' 



EXAMPLES. 



50. How many days elapse between two con- 
junctions of Mercury and Venus ? 
Mercury's daily motion - 4,0928 
Venus' do. 1.6021 



Difference— 2.4907. Then, 
As 2.4907 : 1 : : 360° : 144 days, the time re 
quired. 

5\« How many days elapse between a con- 
junction and an opposition of Venus and Mercu- 
17 ? 

52. How many days elapse between two con- 
junctions of Jupiter and Saturn ? 



92 PLANETARY PROBLEMS. 

53. How many days is Venus a morning and 
an evening star alternately to us ? 

54. How many days is the Earth a morning 
and an evening star alternately to the inhabitants 
ofihe planet Mars? 

55. How many days is Mars a morning and 
an evening star to Jupiter ? 

56. How many days is Saturn a morning and 
an evening star to Herschell ? 

57. How many days elapse between two op- 
positions of Saturn and Mars ? 

58. How many days is Mercury east and west 
of the Sun alternately to us ? 

59. How many conjunctions have the Earth 
and Venus in the period that Saturn and Her- 
schell have two ? 

60. How many days is Jupiter a morning and 
an evening star alternately to us ? 

PROBLEM VI. 

Having the Heliocentric Longitude of any two 
Planets given for any particular day, to de- 
termine when they will be in Heliocentric con- 
junction. 

Rule — If the longitude of the planet which 
is farthest from the Sun, be less than the longitude 
of the planet which is nearest, increase it by 
360°, and subtract the longitude of the nearer 
from the longitude of the farther planet. Then 
say, as the difference of their daily motions 
(taken from the table, page 91) : 1 day : : the 



PLANETARY PROBLEMS. 9.3 

difference of the longitudes last found : days 
reckoned from January 1, when such given 
planets will be in conjunction. 

EXAMPLES. 

61. How many days will elapse after Jan, 1, 
1823, before Venus and Mars will.be in conjunc- 
tion ? 

Solution* — Daily motion of Venus - 1.6091 
Daily motion of Mars - .5240 



Difference 1.0781 



Long, of Mars - - 311° 41' 
Ditto of Venus - - 285° 16' 



Difference 26° 25' 
As 1,0781 : 1 day : : 26° 25' : 24 days after 
Jan. 1, answering to Jan. 25, when these plauets 
will be in conjunction. 

62. On what day in the year 1824, will Jupi- 
ter and Mars be in 6 ? 

63. On what day in the year 1824, will Jupi- 
ter and Saturn be in <5 ? 

64. On what day iu the year 1824, will Ve- 
nus and Saturn be in <$ ? 

65. On what day will Herschell be in 6 with 
the Earth in the year 1824 ? 

66 When will Venus and Jupiter be in <5 id 
the year 1824 ? 

67. When, in the year 1824, will Mars be on 
the meridian at midnight ? 

68. On what day of the year 1824, may I 



94 PLANETARY PROBLEMS. 

expect to see Saturn setting and the Sun rising at 
the same time ? 

69. How many days will elapse after Jan. 1, 
1824? before Mars will set at sun-rising ? 

70. Iu the year 1824, when will Jupiter set 
at sun-rising ? 

71. In the year 1825 in what month will Ju- 
piter be on the meridian of Washington at mid- 
Bight ? 

PROBLEM VII. 

Having a Planet's Heliocentric Longitude for any 
given day give?i, to find its Heliocentric Longi- 
tude for any other day. 

Rules. — 1- Find the number of days between 
the given day and the day required. 

2. Then, as 1 day : the planet's daily motion : : 
the number of days from the given to the requir- 
ed day : to the space the planet has revolved in 
its orbit in that time- This distance, added to the 
planet's longitude on the given day, will be the 
longitude of the planet required. If this sum be 
greater than 360° divide it by 360, so shall the 
remainder be the planet's longitude required. 

EXAMPLES. 

72- What is the longitude of Venus, May 25, 
1824 ? on January 1, it was 150° 2'. 
Solution — From January 1, to May 25, are 145 
days. Then as 1 day : 1.60.21 : : 145 : 232° 18\ 



PLANETARY PROBLEMS. 95 

And 150° 2'+232° 18'=382° 20'. Then 382° 
20'— 360°=22° 20', the longiiUvle required. 

73. Od January 1, 1824, the longitude of Sa- 
turn is 52° 11', what will its loDgitude be August 
22, of the same year ? 

74- On Jan. 1, 1824, the longitude of Jupiter is 
96° 22', what will it be April 24, 1826 ? 

75. What will be the longitude of Mercury, 
June 18, 1825 ? 

76. What will be the longitude of the Earth 
April 27, 1829 ? 

77. What is the Sun's place November 9 t 
1825 ? 

78- What is the longitude of Mars November 
19, 1827? 

79. What is the longitude of Jupiter Novem- 
ber 16, 1825 ? 

80. In what sign of the zodiac must I look for 
ihe planet Herschell, October 16, 1829 ? 

PROBLEM VIII. 

To determine, on any particular Day, whether 
Jupiter or Venus be ihe Morning or the Even- 
ing Star. 

Rule — Find the longitude of Venus or Jupi- 
ter, and the longitude of the Earth for the given 
day. Then if the difference of the longitude of 
the given planet and the Earth, (counting from 
the Earth's place onward,) be less than 180°, the 
planet rises after the Sun and sets after him; and 
is consequently an evening star | but if the said 



96 PLANETARY PROBLEMS. 

difference be greater than 180°, the planet rises 
before the Sun, and is consequently a morning 
star. 



EXAMPLES. 

81- On May 25, 1824, is Venus a morning 
or an evening star ? 

Solution' — The longitude of the earth on May 
25, is, by the last problem 244° 9', and the longi- 
tude of Venus 22° 28'. Then 244° 9'— 22° 28'= 
221° 41', this being more than 180° shows that 
Venus is a morning star. 

82. Is Jupiter a morning or evening star, Aug- 
ust 8, 1824 ? 

83. Is Venus a morning or evening star, De- 
cember 11, 1824 ? 

84. Is Venus a morning or evening star on the 
following days ? 



Jan- 


1. 


1823. 


Dec 6, 1824. 


Oct 


7. 


1825. 


Nov. 7, 1824. 


July 


16. 


1826. 


April 11, 1823. 


Nov- 


9. 


1830. 


Oct- 7,1830. 



85. Does Jupiter rise before or after the Sua 
on November 9, 1824 ? 

86. Does Jupiter rise before or after the Sua 
on May 17, 1823? 

87- Is Venus a morning or evening star July 
18, 1830 ? 

88. During the month of October 1826, is Ju- 
piter or Venus the morniug star ? 



PLANETARY PROBLEMS. 97 

PROBLEM IX. 

To find on what Day any particular Planet 
shall have any given Longitude. 

Rules. — 1. Subtract the longitude of the 
planet on January 1, 1823, from the given lon- 
gitude, taking care to increase the given longi- 
tude by 360° if the longitude on January J, be 
greater than the given longitude. 

2. Divide the degrees last found, (having pre- 
viously reduced the minutes, &c. into decimal 
parts of a degree,) by the planet's tabular daily 
motion; the quotient will be the number of days 
from Jauuary 1, when the planet will have the 
given longitude, 

EXAMPLES. 

89. On what day of the year 1823, will the 
longitude of Venus be 173 c ? 

Solution. 
Given longitude of Venus 171°-f 360°=53S° 
Longitude on Jan. 1. 1823. =?85° 16' 

Difference = 247° 44'=247.7.33S 
Then 247.7.333 

— » — =154 days, answering to Jnue 4th. 

1.6021 

90. On what day of the year 1325 will Mars 
have no longitude ? 

91. When will Herschell be iu 29° £ ? 

92. When will $ be in «p 9° ? 

93. When will Yenus be in X 18°? 

94. When will Saturn enter 25 ? 

95. When will Mars be in 9°y ? 

96. When will the Earth enter $, ? 

9 



§& fcLANETARlT PROBLEMS. 

97. When will Mars be in 7° n ? 

98. On what day of the year 1824 will Jupi- 
ter be in the beginning of q ? 

99. The ascending node of Mercury is 1 ». 
16° 4': when will the planet pass its node in the 
year 1824? 

100. The descending node of Venus is 8 «• 
14° 67' ; when will she pass that node in the year 
1824 ? 

101. The descending node of Mercury is nf, 
16° 4' : when will it pass that node in the year 
1824? 

102. The £>, or ascending node of Mars is tf 
18° 6'; when will Mars be in his node in the 
year 1825? 

103. When will Jupiter next pass his ascend- 
ing node, after the beginning of 1824 ? 

104. When will Saturn next pass his ascending 
node, after the beginning of 1824 ? 

PROBLEM X. 

To find whether either of the inferior Planets can 
transit the Sun in any particular Year* 

Rule — Find (by the last problem) on what 
day the said planet will pass its nodes. Then 
find the Earth's longitude for that day, and if it 
be equal to the planet's longitude, or, which is 
the same thing, equal to the longitude of the plan- 
et's node, the planet will appear to transit the 
Sun ; but if the longitude of the Earth be greater 
or less than the longitude of the planet.it will not 
transit the Sun. 



PLANETARY PROBLEMS, 99 



EXAMPLES. 

105- Will Venus transit the Sun in the year 
1824 ? 

Solution. — The longitude of the ascending node 
of Venus is 75° 8', and by the last problem, she 
will pass that node on June 26, when the Earth's 
longitude is 274° 44', consequently there will be 
no transit then. The longitude of the descend- 
ing node is 255° 8', which node she passes March 
5, when the Earth's longitude is 164° b5\ conse- 
quently Venus will not transit the Sun either in 
passing her ascending or descending node. 

106. Will Mercury transit the Sun in the year 

1824 ? 

107. Will Venus transit the Sun in the year 
1826 ? 

108. Will Mercury transit the Sun in the year 

1825 ? 

109. Will the Earth appear to transit the Sua 
to the inhabitants of Mars in the year 1823 ? 

1 10- Will the Earth appear to transit the Sun 
to the inhabitants of Jupiter in the year 1824 ? 

PROBLEM XL 

To find when any two given Planets shall have a 
given Heliocentric Aspect their Longitudes 
on January 1, 1823, being considered given. 

Rule.— Add the degrees in the given aspect 
to the longitude of either of the planets, and 



100 PLANETARY PROBLEMS. 

then take the difference of that sura, and the lon- 
gitude of the other. 

Then, as the difference of the daily motions of 
the two planets : 1 day : : the difference found 
above : the time required. 

EXAMPLES. 

Ill At what time in the year 1824, will the 
Earth and Venus have a trine aspect ? 

Solution. — Long, of Venus, Jan. 1, 150° 2*, 
Earth's long. 100° 6'. To the Earth's long, add 
120°, the sum is 220° 6' :— 

220°. 1 -150°.0333 70°.0667 

Then = = 113 + 

1.6021 -.9856 .6165 

days, answering to April 23, nearly. 

112. When will Saturn and Herschell have a 
sextile aspect ? 

113. When in the year 1824, will Mars and 
Jupiter have a quartile aspect, their longitudes 
on Jan. 1, being given ? 

114. When will Jupiter and the Earth be in 
conjunctiou in the year 1 824 ? 

115. When will the Sun and Saturn have a 
trine aspect in the year 1824 ? 

116. When will Venus and Mars have a quar- 
tile aspect, in the year 1826 ? 

117. When will Saturn and Herschell have a 
sextile aspect, after January 1st. 1824 ? 

PROBLEM XII. 

To find the Geocentric Place of any Planet on 
any particular day. 

Rule. — Find the longitude of the Earth and 
the planet, for the given day : lay a ruler over 



PLANETARY PROBLEMS. 101 

the planet and Earth's place in the solar system 
(Plate VII. Fig. 5.) ; and where the ruler in- 
tersects the zodiac, is the geocentric place of the 
planet. 

EXAMPLES. 

1 1 3. What is the geocentric place of Mercu- 
ry, January 1st. 1821 ? 

Solution. — The longitude of the Earth is 3 s . 
10°, and of Mercury 6 s . 21°; a ruler laid over 
these poiuts in their respective orbits will cut the 
zodiac in £ 19°, the geocentric place of Mer- 
cury, as required. 

119. What is the geocentric loDgitude of Sa- 
turn, April 17, 1821 ? 

120. What is the geocentric longitude of Ve- 
nus, November 9, 1 822 ? 

121. What is the geocentric longitude of Ju- 
piter, August 19, 1824 ? 

122. What is the geocentric longitude of 
Mars, December 28, 1828 ? 

123. What is the apparent place of M^rcury 5 
October 6, 1821 ? 



m 



102 



PART III. 



0EOGRAPHICAL AND ASTRONOMICAL 
PROBLEMS, TO BE PERFORMED BY THE 
0LOBES. 



THE TERRESTRIAL GLOBE. 



Description of the various Parts of, and the 
Lines drawn en, " The Terrestrial Globe" 

265. The terrf stria! globe is a globe or sphere, 
made to represent the Earth, on which the king- 
doms, oceans, towns, seas, &c. are depicted, ac- 
cording to their sizes, situations, &c. 

266. This globe is, for convenience's sake, 
fixed in a frame, the upper flat part of which, is 
denominated the wooden horizon, and is divided 
into three concentric circles. 

267. The outermost circle of the wooden hori- 
zon, is divided into twelve parts, in which the 
months, and the number of days each month con- 
tains is written. 



THE TERRESTRIAL GLOBE, 103 

268< The middle circle contains the naraes,and 
the order of the twelve signs of tire zodiac ; and 
is so placed, that the day the Sun enters any par- 
ticular sign or degree of the ecliptic, is opposite 
that sign or degree. 

Obs. — Against January 1st. in the outer circle, is 11® 
VJ, that is, on January 1st. the Sun is in VJ ll°,and as 
the Earth is always in the opposite part of the ecliptic 
to the Sun, it is in 03 11°. 

269. The innermost circle is divided into four 
parts, each containing 90°; around which are 
placed the points of the mariner's compass. 

270. The brazen circle, which encompasses 
the globe, and is useful in keeping the globe 
steadily in its frame, is called the brazen meri- 
dian, and is divided into 360°. 

271. The two brass circles which are placed 
on the globe, and fixed at opposite points of the 
brazen meridian, are called hour circles ; each 
is divided into 24 parts, to represent the hours 
in a day. 

272. From the centre of one of the hour circles 
to the centre of the other, is fixed a wire, which 
goes quite through the globe ; on this wire it 
turns, and this is called the axis of the globe. 

273. The two extreme points of this axis, 
which are fixed in the brazen meridian, are call- 
ed poles ; one is denominated the north, and the 
other the south pole. 

274. Upon the surface of the globe are drawn 
various lines, which geographers have iuvented 
for the more easily distinguishing the different 
parts of the Earth. 

275. Some of these lines are drawn on the 



104 PROBLEMS PERFORMED BY 

globe, in the direction of the brazen meridian,and 
encircle the globe, passing through both poles, 
and are called meridians. 

There are 24 meridians drawn on the surface 
of most globes. They are consequently 1 5° as- 
sunder. 

Obs. — Each of the meridians divides the globe into two 
equal parts; and they are, on that account, called great 
circles. 

276. The lines which are drawn perpendicu- 
larly to these meridians.and encompass the globe, 
are called almacantars, or parallel circles ; they 
are all perpendicular to the meridians,and paral- 
lel to each other. 

277. The circle which is in the middle of the 
globe, and equally distant from each pole, and 
divides it into two equal parts, is called the e- 
quator. 

. 278. The parallels are generally placed 10° 
asunder; so that there are eight parallels north, 
and eight south of the equator. 

G6s. — Each of these parallels divides the globe into two 
tin equal parts ; they are, therefore, called small circles, 
to distinguish them from the circles which divide the 
globe into two equal parts or great circles. 

279. At 231° on each side of the equator, are 
drawn two small circles, which are called tropic- 
al circles, or tropics- The northern is called 
the tropic of Cancer, and the southern the trop- 
ic of Capricorn. 

280- At 23^° distant from each pole, are like- 
wise drawn two small circles. That encircling 
the north pole, is called the Arctic Circle, and 
that encircling the south pole, the Antarctic Cir- 
cle. 



THE TERRESTRIAL GLOBE. 1©5 

Qbs. — These circles divide the globe into five zone?. 
1. The North Frigid Zone. included between the north 
pole and the arctic circle. 

2. The South Frigid Zone, included between the 
south pole and the antarctic circle. 

S, The North Temperate Zone, comprehended be- 
tween the arctic circle and the tropic of Cancer. 

4. The South Temperate Zone, contained within the 
arctic circle and the tropic of Capricorn. 

5. The Torrid Zone, contained within, and bounded 
by the tropics. 

281. The equator is numbered by degrees, 
from the meridian which passes through London, 
east and west round the globe, until such num- 
bers increase to ] 80°. 

282. The apparent path of the Sun through 
the zodiacal signs, called the ecliptic is like- 
wise drawn thereon. The ecliptic is a great 
circle which intersects the equator in two oppo- 
site points, and is divided like the middle circle 
of the wooden horizon, into twelve parts ; these 
signs, viz. T Aries, & Taurus, n Gemini, 
25 Cancer, & Leo, ti# Virgo, =£= Libra, n\ Scor- 
pio, / Sagittarius, xz Aquarius, X Pisces, are 
marked thereon. 

283. The quadrant of altitude is a thin slip 
of brass divided into degrees It is so contrived 
as to be capable of being fixed to any part of the 
brazen meridian. 

284. The analemma is a projection of the 
sphere upon the meridian. This accompaniment 
is particularly useful in readily determining the 
Sun's declination on any particular day : which 
days are of an equal length, &c. &c. 



306 PROBLEMS PERFORMED BT 

GEOGRAPHICAL AND ASTRONOMICAL 
DEFINITIONS. 

285. The latitude of any place on the terres- 
trial globe, is its perpendicular distance from the 
equator, measured in degrees, and can never ex- 
ceed 90°. 

286. The longitude of any place on the globe 
is its horizontal distance from the meridian of 
London, measured on the equator,and can never 
exceed 180°. 

287. The zenith of any place is the point im- 
mediately over head, and the nadir the point di- 
rectly under feet The zenith and nadir are the 
two poles of the horizon, each being 90° distant 
therefrom. 

288. The Sun's place in the ecliptic, is the 
portion of the ecliptic in which the Sun appears 
as viewed from the Earth, and is exactly six 
signs distant from the Earth's place. 

289. The declination of the Sun on the globe 
Is the nearest distance of the Sun's place from 
the equator. 

200. The amplitude of any celestial body, is 
the distance it rises from the east, and sets from 
the west, measured on the horizon. 

291 A vertical circle is an imaginary circle 
passing through the zenith and nadir, cutting the 
horizon at right angles. On this circle the alti- 
tudes of the celestial bodies are measured, and it 
is illustrated by the quadrant of altitude fixed in 
the zenith. 



THE TERRESTRIAL GLOBE. lO? 

292. The right asceusion of any celestial body, 
is the distance of the meridian, which passes 
through that body, from the first point of Aries, 
measured on the equator. 

Obs. — The right ascension of the Sun, is the distance 
of the meridian, which passes through the Sun's place, 
from the first point of Aries, measured on the equator. 



GEOGRAPHICAL AND ASTRONOMICAL 
PROBLEMS, ON THE TERRESTRIAL GLOBE. 



PROBLEM I. 

To determine the Latitude of any Place on the 
Globe. 

Rule. — Bring the given place, to that part 
of the brass meridian which is numbered from the 
equator towards the poles ; the degree on the me- 
ridian opposite the said place, is its latitude re- 
quired. 

EXAMPLES. 

1. What is the latitude of Plymouth ? 
Ans. 50-| o N. 

2. What is the latitude of each of the follow- 
ing places ? — Athens, Aberdeen, Archangel, 
Astracan, Berlin. Boston, Brest, Bristol, Cadiz, 



108 PROBLEMS PERFOKMEB BY 

Cape of Good Hope, Copenhagen, Dover, Dub- 
lin, Edinburgh, Elba, Finisterre (Cape), Glas- 
gow, Helena(St ), Ispahan, Lima, London, Mad- 
ras, Naples, Oporto, Portsmouth, Quebec, and 
Vienna. 

3. What places ou the Earth have the same 
latitude as Cape Horn, Stockholm, and Buda ? 

4. What inhabitants of the Earth, have their 
days of the same length as those of Plymouth, 
Cagliari, and Grand Cairo ? 

PROBLEM II. 

To find the longitude of any given Place. 

Rule. — Bring the given place to the brass 
meridian, and observe the number of degrees 
marked on the equator, under the brass meridian, 
which is the required longitude of the given 
place. 

Note. — If the numbers on the equator are increasing 
from (lie left towards the right hand, the longitude is 
east; if from the right towards the left hand, it is west. 

EXAMPLES. 

What is the longitude of Plymouth ? 
Am. A\° W. 

What is the longitude of Dover ? 
Ans. 1° E. 
5, Required the longitudes of the following 
places : — Aberdeen, Barbadoes, Canton, Buda, 



THE TERRESTRIAL GLOBE. 10S 

Gibraltar, Lisbon, Nankin, Jeddo, Cape Como- 
rin, and Philadelphia. 

6. What places on the Earth have the same 
longitudes as Palermo, Alexandria, and Cork ? 

7. To what places on the Earth is the Sua 
south the same time it is at Plymouth, Paris, and 
Madrid ? 

8. What places on the Earth have midnight, 
the same time as the inhabitants of Plymouth, 
Irkutsk, Tobolsk, and Stockholm ? 

9. What places on the Earth have their hours 
at the same time as the inhabitants of London, 
and Versailles ? 

10. What places on the Earth have no longi- 
tude ? 



PROBLEM III. 

Having the Latitude and Longitude of any 
Place given, to find that Place. 

Rule. — Bring the given longitude, found on 
the equator, to that part of the brass meridian 
which is numbered from the equator towards the 
poles, and under the given latitude, on the brass 
meridian, is the place required. 

examples. 

What place is that whose latitude is 50^° N. 
and longitude 4£° W. 
Ans. Plymouth. 



10 



110 



PROBLEMS PERFORMED BT 



11. What places have the following latitudes 
and longitudes ? 



Latitudes. 


Longitudes. 




50° " N* 


6° W. 




56 N. 


671 W. 




6i S. 


107 E. 




3| S. 


1021 E. 




64' N. 


39 E. 




58 1ST. 


9 W. 




39 N. 


771 W. 




221 JNT. 


881 E. 




- 







12. What place is that whose latitude is as 
much south as Plymouth is north, and whose lon- 
gitude is as much east as Plymouth is west ; the 
inhabitants of that place have their feet against 
those of the inhabitants of Plymouth,and are call- 
ed Antipodes ? 

PROBLEM IV. 

To find the Difference of Latitude of any two 
Places. 

Rule- — Find the latitude of each place by 
Problem I. and if they are both north, or both 
south, their difference will be their difference of 
latitude sought ; but if one is north,aud the other 
south, their sum will be their difference of lati- 
tude required. 



THE TERRESTRIAL GLOBE. Ill 



EXAMPLES. 

What is the difference of latitude between Ply 
mouth and Rome ? 

Plymouth, - 501° N. 
Rome, - - 41 K. 

Ans. 9±° Dili*, required. 



What is the difference of latitude between 
London and Cape Horn ? 

London, - 5H°N. 

Cape Horn, - 56" S, 

Ans. 107J° Biff required. 

13. What is the difference of latitude between 
the following places ? 



London and Paris, 
Madrid and Buda t 
Petersburgh and Turin, 
Copenhagen and York, 



Pekin and St. Salvador, 
Washington and Calcutta 
Berlin aixl Bristol, 
Cork and Moscow. 



14. How many degrees is Moscow north of 
Piymouth ? 

15. What two places on the globe have the 
greatest difference of latitude ? 

PROBLEM V. 

To find the Difference of Longitude of any two 
Places. 

Rule. — Find the longitude of each place by 
Problem II. : and if they are both east or both 



112 PROBLEMS PERFORMED BY 

west, the difference between the greater and the 
lesser longitudes will be their difference of longi- 
tude required ; but if one is east and the other 
west, the sum of their longitudes will be their dif- 
ference of longitude sought. 

Note. — If the sum of their longitudes be greater than 
180°, subtract it from 360°, and the remainder will be 
the difference of longitude. 

What is the difference of longitude between 
Plymouth and Cork ? 

Longitude of Cork, 8J° W. 

Longitude of Plymouth, A\ W. 

Ans. 4i° 

4 

What is the difference of longitude between 
Cape St. Roque and Bombay ? 

Long, of Cape St. Roque - 35° W. 
Long, of Bombay - - - 71 E. 

Ans. 106° Diff 



16, What is the difference of longitude be- 
tween the following places ? 

London and Baltimore, { Syracuse and Malta, 

Copenhagen and the Lizard, I Calcutta and Cadiz, 

Jeddo and Mocha, Brest and Inverness, 

Baku and Buda, Rome and Cape Horn, 

Surinam and Palermo, Candi and the Lizard. 



THE TERRESTRIAL GLOBE. 1 13 

17. What is the greatest difference of longitude 
any two places can have, and name four places 
which are so situated ? 

PROBLEM VI. 

Paving the Time at any particular Place given, 
to find the time at any other Place- 

Rule, — Bring the given place, and the given 
hour on the hour circle, to the brass meridian, 
and turn the globe until the proposed place is un- 
der the meridian, the hour cut k thereby is the 
time required. 

Or, ivithout a Globe. 

Divide the difference of longitude of the two 
places by 15, and the quotient will be their dif- 
ference of time- If the place to which the time 
is required be east of the other, add; if to the 
west, subtract their difference of time to or from 
the time given ; and the sum or remainder will 
be the time required- 

EXAMPLES. 

When it is 12 o'clock at London, what is the 
time at Dresden ? 

Ans. 11 hr. P.M. 
18. When it is 4 o'clock P- M- at London, 
what is the time at Paris ? 

19. What is the time at Buda, when it is 7 
his. 16 mm. A. M-at Madrid ? 

10* 



114 PROBLEMS PERFORMED BY 

20 What is the hour at Barcelona when it is 
noon at Calcutta ? 

21. When it is midnight at New- York, where 
is it noon ? 

22. What places on the Earth are 45° E. of 
London ? 

23 When it is noon at Edinburgh, to what 
places has the sun passed the meridian two 
hours ? 

24. What places have their time two hours 
earlier than the inhabitants of Aberdeen ? 

25. In an eclipse of the moon it was observed 
to begin at London 11 hrs. 37 miu. P. M. what 
time did it commence at Moscow and at Dub- 
lin ? 

26. What places have their time the same as 
the inhabitants of Madrid ? 

27. When it is midnight at Mecca, where are 
the people dining, supposing they dine at 1 
o'clock, P. M. 

28. On September 1st. 1821, 3 hrs- 47 min. 
A. M. Jupiter's first satellite was eclipsed at 
Loudon; what is the longitude of that place, 
where the said eclipse began at midnight ? 

PROBLEM VII. 

To find the Distance of any two Places on the 
Globe, 

Bulk- — Lay the graduated edge of the quad- 
rant over the two places, and the degrees be- 
tween them, multiplied by 69J, will be their dis- 
tance in English miles- 



THE TERRESTRIAL GLOBE. 115 

EXAMPLES. 

What is the distance between Plymouth and 
Paris ? 

Ans. 4°, or 278 miles. 

29. What is the distance between the follow- 
ing places ? 

London and Rome York and Bucfa jSt.Helena&Cadiz 
Paris and Palermo Cork and Dover JPekin & Madrid 
Moscow& Stockholm Oporto & Jeddo Uspahan & Ivica. 

30. How long would a ship be sailing from 
Plymouth to Philadelphia, at the uniform rate of 
3 miles per hour ? 

PROBLEM VIII. 

To find the Aniceci, Perioeci, and Antipodes cf 
any given Place. 

Definitions. — 1. The Antceci are those who 
live in the same latitude and longitude, only one 
has north latitude and the other south. 

2. The Perioeci are those who have the same 
latitude and opposite longitudes, 

3. The Antipodes are those who have opposite 
latitudes and longitudes. 

Rule. — Bring the given place to the brass 
meridian, and the Antceci, Perioeci, and Anti- 
podes, may be found immediately by attending 
to the above definitions. 

EXAMPLES. 

What are the Antreci, Perioeci, and Antipodes 
of London ? 



116 TEOBLBMS PERFORMED BY 

Ans. Antoeci, the inhabitants of the South Sea^ 
east of the Sandwich Islands. 

Periceci, the inhabitants of the islands of the 
Northern Archipelago, 

Antipodes, the inhabitants of the lowest ex- 
tremity of 3New Zealand. 

31. What are the Antoeci of Petersburg!); the 
Periceci of Madrid, and the Antipodes of Cal- 
cutta ? 

32. If a hole were to be bored from Phila- 
delphia through the centre of the earth and con- 
tinued, in what part of Europe would the cavity 
*)e? 

PROBLEM IX. 

To rectify the. Globe, or to put the Globe in such 
a position as the Earth actually is, on any giv- 
en Day at Noon ; to tell the Sim's Declina- 
tion and right Ascension ; or to find on what 
Day the Sun has any given Declination. 

Rules.- — 1 . liaise or depress the pole in such 
a manner that it may be so many degrees above 
the horizon, as are equal to the latitude. 

2. Find the day of the month in the outer 
circle of the wooden horizon ; and against it, in 
the middle circle, is the Sun's place in the eclip- 
tic. 

3. Find the corresponding Sun's place in the 
ecliptic, which bring to that part of the brass me- 
ridian numbered from the equator towards the 
poles : and put 12 on the hour circle to 



THE TERRESTRIAL GLOBE. 11? 

said meridian. The globe is then rectified as 
required. 

4. The decree od the brass meridian, directly 
over the Sun's place, or against the given day, 
on theanalemma, is the Sun's declination ; the 
degree on the equator, cut by the brass meri- 
dian, is his right ascension ; and the day answer- 
ing to any given declination is the day on the 
aualemma, or the day answering to the Suu's place 
in the ecliptic, immediately under it. 

EXAMPLES. 

Rectify the globe for London, May 1 4th, at 
noon ? 

Solution. — 1 . Let the north pole be elevated 
b\\° above the horizon. 

2. Against May 14th, on the outer circle of the 
horizon, is 8 24°. 

3. Then tf 24° on the ecliptic, being brought 
to that part of the brass meridian which is num- 
bered from the equator towards the poles, and 12 
on the hour circle being brought there also, the 
globe is rectified as required : his declination is 
about 18° N. and his right ascension 52°. 

33. Rectify the globe for New-York, July 
8th. and tell me the Sun's declination and right 
ascension. 

34. Rectify the globe for Madrid,and tell me 
th e day the Sun has 19|° JN". declination. 

35. Rectify the globe tor Oporto, January 8th. 
and tell me the Sun's declination, right ascension. 
&c. 



118 PROBLEMS PERFORMED BY 

36. Rectify the globe for Madras, and tell me 
the day the Sun's declination is 20° S. 

37. Rectify the globe for Cape Horn,Decem- 
ber 21st- and tell me the Sun's declination. 

38. What is the difference betweeu the lati- 
tude of Gibraltar, and the Sun's declination Jan- 
uary 4th ? 

39. How many degrees difference is there in 
the altitude of the Sun at London, January 6th. 
and April 4th ? 

40. How many degrees is the Suu apparently 
lower at Vienna on December 21st than on June 
21st? 

41. How many degrees colder is it at Madrid 
on October 4th than on July 6th ? 

42. If the Sun's rays shine 90° from its declin- 
ation, to what degree of north latitude will it ex- 
tend on February 4th ; and what is his right as- 
cension on that day ? 

43. To what degree of north latitude will the 
Sun extend on December 21st ? 

44. How many degrees will the Sun's rays ex- 
tend over the north pole, on April 18th ? 

45. On what day will the inhabitants of Spitz- 
l^ergen begin to receive the Sun's rajs,after hav- 
ing been involved in gloomy twilight ? 

46. On what day is the Sun's right ascension 
85°? 



THE TERRESTRIAL GLOBE- 119 



PROBLEM X. 

To find the Places on the Earth where the Sun is 
vertical ; what Places are deprived of the Sari's 
Rays ; and those that have constant Sunshine, 
on any given Day. 

Rule. — Find the Sun's declination by the last 
problem, and note it on the brass meridian : turn 
the globe on its axis, and all the places which 
pass under the Sun's declination will have the 
Sun vertical on the given day* To ail places 
more than 90° distant from the Sun's place, it 
will not shine on that day. 

Or, bring the Sun's declination to the zenith, 
and turn the globe on its axis; the places passing 
under the declination will have the Sun vertical ; 
those which do not descend below the horizon 
will have constant day ; and those which do not 
come above the horizon have constant night. 

EXAMPLES. 

On May 4th, to what places of the Earth is 
the Sun vertical ; where does he not shine ; and 
what places have constant day ? 

Ans> — The Sun is vertical to the inhabitants 
of Acapulco, Guadaloupe, Hydrabad, &c. &c. 
he does not set to the inhabitants of Nova Zem- 
bia, Spitzbergen, &c. and he does not shine at all 
to all places within 15° of the south pole. 

47. To what places is the Sun vertical, July 



120 PROBLEMS PERFORMED BY 

] 6th ; and what parts of the Earth have perpetual 
suoshine ? 

48. To what places on the Earth does the Sua 
not shine on November 12; where is he verti- 
cal; and what places have constant day-light ? 

49. What inhabitants of the Earth have no 
shadow when the Sun is on the meridian, April 
18th? 

50, What inhabitants of the Earth have the Sua 
visible in the north, on December 16th ? 

51. Is the Sun ever vertical to the inhabitants 
of Calcutta ; if so, on what days ? 

52- How many degrees does the Sun over- 
shadow the south pole on May 16th : how much 
south of Plymouth is the place where he is ver- 
tical ? 

53- How many degrees south of St. Peters- 
burg, is the place where the Sun is vertical on 
April 8th ? 

54. How much farther north is that place 
where the Sun does not set, ou May 18th, than 
Brest is ; and what is the difference of latitude 
between London and the place where the Sun is 
vertical, on that day ? 

PROELEM XL 

To find where the Sun is vertical ; to what Places 
he is rising ; and to what Places he is setting 
at any Time on a given day^ at a given Place. 

Rules — 1 -Bring the given place, and the given 
hour, on the hour-circle, to the brass meridian* 



$&£ TERRESTRIAL GLOBE* I2l 

2. Find the Sun's declination, and note the de* 
gree on the brass meridian equal thereto. 

3. Turn the globe until 12 at noon comes to 
the brass meridian ; then to the place under the 
Sun's declination,the Sun is vertical: to the places 
on the eastern edge of the horizon, he is rising ; 
to those on the western edge he is setting ; and 
to those places which are in the north and south 
parts of the horizon, the Sun appears in the hori* 
zon the whole day, 

EXAMPLES. 

When it is 7 o'clock A. M. at London, July 
Bth, where is the sun vertical ; to what places is 
he rising and setting; and where does he continue 
in the horizon the whole day ? 

Am. The Sun is vertical at Burhampour % 
he is rising to the Solomon Islands, east of New 
Guinea; he is setting to the west coast of Africa, 
Cape Verd, &c. and he appears in the horizon 
the whole day to the northern parts of Hudson's 
Bay, &c. 

55. When it is 5 hrs. A* M. at Plymouth* 
April 8th, where is the Sun vertical, rising and 
setting, &c. 

56. When it is 9 hrs. 30 ; P. M at Madras, 
Nov. 6, where is the Sun rising,set!ing, and ver< 
tical ? 

57. When is it 8 hrs. A- M. at Petersburgh, 
August 4th, where is it midnight ? where is the 
Sun vertical, rising and setting? 

58. Where is the Sun in the zenith, April 
17th, when it is 4 hrs. P. M. at New- York J 

It 



122 PRQBLEMS PERfrORMEB BY 



PROBLEM XII. 

To find (he Time the Szin rises and sets ; the 
Length of his diurnal and nocturnal Arcs; hisr 
oblique Ascension and Descension ; with the 
Length of the Bay and Night, on any particu- 
lar Day, at a given Place. 

Rules.— 1- Rectify the globe for the latitude 
and Sun's place, by Problem IX. 

2. Bring the Sun's place to the eastern edge 
of the horizon ; the degree on the equator, cut 
by the horizon, 4s Ills oblique ascension; and the 
hour on the hour-circle, cut by the brass meri- 
dian, is the time he rises : bring the Sun's place 
to the western edge of the horizon, the degree of 
the equator cut thereby is his oblique descen- 
sion ; and the hour on the hour-circle under the 
brass meridian the time he sets : double the time 
©f the Sun's rising,and it will be the length of the 
night ; double the time of his setting, and it will 
be the length of the day ; multiply the length of 
the day by 15°, and it will be the Sun's diurnal 
arc; multiply the length of the night by 15°, and 
it will be the length of his nocturnal arc. 

Or, by the Analcmma. 

Elevate the pole to the latitude ; bring the 
middle of the analemma, and 12 on the hour- 
circle, to the brass meridian ; turn the globe 
eastward, until the given day comes to the 
horizon, and the hour-circle will show the time 



I HE TERRESTRIAL GLOBE. 123 

the Sun rises ; bring the given day to the 

western edge, and it will show the time he 
sets. 



Note. I. — If -he time the Sun rises be taken from 12 
hours, it will leave the time he sets: because he rises as 
long before noon, as he sets after noun. 

2. The difference between the right and oblique as- 
cension, is the ascensional difference; which, converted 
into time, at 15° an hour, is the time the bun rises and 
sets, from six o'clock. 



EKAMFLES. 

At Madras, August 16th, what time does the 
Sun rise and set ; what is his oblique ascension 
and descension, the lengths of the day and night, 
and the lengths of his diurnal and nocturnal arcs? 

Ans. The Sun rises at 5| hrs. sets at ££ ; the 
length of the day js 13 his. and of the night II 
hrs. ; hi? nocturnal arc is 15°xl 1 = 165°, and his 
diurnal arc 13x1 5°== 195°; his oblique ascension 
is 144°, and his oblique descension 151°. 

60 What time does the sun rise and set, oo 
3uh 18th, at Petersburg!!? 

61 What is the length of the day, the Sun's 
oblique ascension and descension, and his diurnal 
and nocturnal arcs, on June 21, at London ? 

62= What is the difference in the lengths of the 
longest and shortest days at York ? 

63. What is the length of the Sun's diurnal arc 
at Calcutta, July 17th? 

64. How much longer is the day at Nc-rtb 
Cape than at Plymouth, August 16th ? 



124 PROBLEMS PERFOEMEDBY 

65. What is the length of the night at Peters- 
burg!], oo December 21st ? 

66. How much longer is the day at Plymouth 
than at Paris, on April 4th ? 

67. What time does the Sua rise and set at 
Madagascar, on July 8th ? 

68. What is the length of the longest and 
shortest days at London, Paris, Alexandria, and 
4Jeppo ? 

PROBLEM XIII. 

To find how long the Sun continues above or be- 
low the Horizon, to any Place in the Frigid 
Zones. 

Rule, — Subtract the latitude of the givea 
place from 90°, the remainder will be the Sun's 
declination, when constant day begins and ends 
there; the space of time elapsing between the days 
answering to the Sun's declination, will be the 
time the Sun continues above or below the hori- 
Son, at the givea place. 

EXAMPLES. 



How many days does the Sun illuminate the 
southern part ot Nova Zambia, latitude 70° N. 

Solution. 90° - 70°=20°, the Sun's declina- 
tion when he begins constantly to shine there. 
The days answering to 20° JN\ declination are ? 
May 21st and July 23do From May 2 1st to 



THE TERRESTRIAL GLOBE. 125 

July 23d, are 63 days; the time the Suu contin- 
ues above and below the horizon at the given 
place. 

69. Captain Parry,and the crew of the British 
ship Griper, when searching for a north west pas- 
sage to India, in the year 1319, wintered in Baf- 
fin's Bay, in latitude 76° IN", how long were they 
deprived of the sight of the Sun ? 

70. How long does the Sun shine constantly to 
a place in latitude 72^-° N. ? 

PROBLEM XIY. 

To find the Sun's Altitude and Azimuth, en any 
Day, at any Place and Hour ^and his Meridian 
Altitude. 

Rules.-— 1. Rectify the globe for the latitude 
and Sun's place, by Problem IX. 

2. Fix the quadrant in the zenith,turn the globe 
until the given hour is under the brass meridian ; 
lay the quadrant over the Sim's place, and the 
number of degrees thereon is the Sun's altitude* 
at the given hour. 

3. The number of degrees in the inner circle 
of the horizon, from the point where the quadrant 
intersects it to the south, is the Sun's azimuth. 

4. The number of degrees from the Sun's de- 
clination, on the brass meridian to the horizon, is 
the Sun's meridian, or greatest altitude, 

Note — The rule by the analemma is the same ; only, 
bring the middle of the analemma, instead of the Sun's 
place to the brass meridian, and use the given clay, as* 
you used the Sun's place in the ecliptic, 

n* 



I2g FEOBLEMS PERFORMED B^ 



EXAMPLES. 

What are the Sun's altitude and azimuth ox* 
January 8th, 10 hrs. A. M. at London ? 

Ans. The Sun's altitude is 12°, and his azi- 
muth, S. 25 E. 

71. What is the Sun's meridian altitude at 
Cork, April 13th? 

72. What is the Sun's azimuth and altitude at 
10 o'clock, A M. at Barbadoes ? 

73. What is the Suu's altitude at 6 o'clock, 
A. M. on July 5th, at Vienna ? 

74. What are thr Sun's greatest and least me- 
ridian altitudes at London ? 

75. June 10th, at Cape Comorin,required the 
time of the Sun's appearing twice on the same 
azimuth. 

76. What are the azimuth and altitude of the 
Sun, when bis declination is 18° S. at 11 hours, 
A. M. at Madrid ? 

77. What is the altitude of the Sun at Pondi- 
cherry, at 9hrs. A. M. \pril 18th ? 

78. What is the Sun's azimuth, at 9 A, M. Ju- 
ly 8?h, at Buda, with his meridian altitude there 
on that day ? 

PROBLEM XV. 

To find the Sun's rising and setting Amplitude, 
on any given day. 

Rule.-— Rectify the globe for the latitude anct 
Sun's place, by Problem IX. 



TJIE TEfiREBTRIAL GLOBE, 1.27 

Turn the globe until the Sun's place comes to 
the eastern edge of the horizon ; and the number 
of degrees on the inner circle, counting from the 
east, is his rising amplitude : bring the Sun's 
place, to the western edge of the horizon, and the 
number of degrees on the inner circle, counting 
from the west, is his setting amplitude. 

Note. — The rule by the analemma is the same ; only, 
bring the middle of the anaiemma, instead of the Sun's 
place, to the brass meridian ; and use the given day, as 
you used the Sun's place in the ecliptic, 

EXAMPLES. 

What is the Sun's rising amplitude, on April 
18th, at London ? 
Ans. E. 20° N. 

79. What is the greatest rising amplitude the 
Sun has, at Paris ? 

80. How many degrees does the Sun set from 
the west at Oporto, December 16 ? 

81. Does the Sun rise to the north or south of 
the east, at Palermo, July 1 9th ? 

82. What are the Sun's rising and setting am- 
plitudes,at Moscow, November 24th ? 

83. What time does the Sun rise at Lisbon* 
Nov. 8th ; and what is his setting amplitude ? 

84. July 1 7th, the Sun's amplitude was observ- 
ed to be E. 18 N. ; what was the latitude ? 

85. Nov. 22d, the Sun's amplitude was observ- 
ed to be E. 29 S.$ what was the latitude ? 



,223 MOSLEMS PEEFOBMED BY 



PROBLEM XVL 

To find the Beginning, End, and Duration of 
Twilight, at any given place, on a given Day. 

Rules — 1. Rectify the globe, the latitude, and 
sun's place, by Problem IX. 

2. Fix the quadrant in the zenith, and turn 
the globe east, until the Sun's place touches 18® 
on the quadrant below the horizon ; the hour on 
the hour-eircle, under the brass meridian, is the 
time the twilight begins in the morning : turn the 
globe west, and proceed as above directed, and 
you will obtain the time the twilight ends in the 
evening. 

The duration of morning twilight, is the time 
from its commencing until sun-rising ; or the du, 
ration of evening twilight, is the time from sun- 
setting, to the time the Sun takes to descend !8« 
perpendicularly below the horizon, [f the Sua 
does not descend 18° perpendicularly below the 
horizon, twilight will continue from sun-setting 
to sun rising, and there will be no night. 

Note. — The rule bv the analemma is the same, only, 
brtng the middle of the analemm, instead of the Sun's 
place, to the brass meridian ; and use the given day, as 
you used the ^un's place in the. ecliptic. 

EXAMPLES. 

At what hour does morning twilight begin and 
end, at London, February 19th? 



$HE TERRESTRIAL GLOBE. 129 

Arts. Day -light commences at 5 hre. A.M. and 
ends at 7 hrs. P. M. 

86. At what time does the morning twilight be" 
gin at Moscow, September 19th ? 

87. At what hour does darkness encompass the 
atmosphere of Washington, March 29th ? 

88. How many hours from day-break to sun- 
setting at, Baden, November 9th ? 

89 How long does twilight continue at Cal- 
cutta, September 7th ? 

90. What is the length of twilight at Cam- 
bridge, October 13th? 

91. What is the difference in the length of 
the twilight on April 4th, and November 1st, at 
London ? 

92 What is the difference in the length of the 
twilight at Malta and Plymouth, on April 3d 2 

PROBLEM XVII. 

■To find the Beginning, End, and Conti?watio7i K 
of constant Day, at any given Place. 

Rules — 1 . Add 1 8° to the given latitude. 
2, Subtract that sum from 90°, and the remain- 
der will be the San's declination, when constant 
day begins ; the space of time elapsing between 
the days corresponding to the Sun's declina- 
tion, will be the time that constant day continues 
at the given place. 

Nuie. — If the sum of the latitude and 18° be more thaR 
90°, subtract 90° from that sum, and the remainder will 
be the Sun's declination 5 of a eoutrary nam© t® the latii* 
tude. 



130 PROBLEMS PERFORMED BIT 



EXAMPLES. 

When does constant day begin, and how long 
does it continue, at London ? 

Solution.— The lat. of London 51£°N. Then 
51|° + 18° =691°. And 90°— 69i = 20^= 
the sun's declination when constant day begins 
and ends ; the days answering to which are May 
23d, and July 20th ; the space of time between 
these days is 58 days, the time required. 

93. At Petersburg!), when does constant day 
begin, and how long does it continue ? 

94. At Greenland, when does constant day 
begin, and how long does it continue ? 

95. At Labrador, when does constant day be- 
gin, and how long does it continue ? 

96. At the North Pole, what is the duration 
of twilight ? 

97. At North Cape, what is the duration of 
twilight ? 

PROBLEM XVni. 

To find the days when the Twilight is the short* 
est in any given Latitude. 

Rules — h Elevate the pole to the latitude. 

2. Bring the first degree of Libra on the eclip- 
tic to the eastern eoge of the horizon, and fix 
the quadrant on the zenith. Keep the globe 
steady, and bring 18° on the quadrant to touch 
the ecliptic under the horizon : the day corres- 
ponding to the sun's place, cut by 18° on the 
quadrant, is the day required. 



THE TERRESTRIAL GLOBE. 131 



EXAMPLES. 

At Cambridge*, latitude 52 J°, N. on what day 
of the year is the twilight shortest ? 

Solution. — The globe beiog elevated to 52±° 9 
the latitude of Cambridge ; the quadrant being 
screwed in the zenith, and 1° of Libra brought 
to the eastern edge of the horizon; 18° on the 
quadrant will cut the ecliptic under the horizon 
in 20° of Libra, the day answering to which is 
October 12th, and the day when the sun's decli- 
nation is the same as October 12th, is March 
LM,the two days when twilight is shortest at Cam- 
bridge. 

93. At Plymouth, on what days is the twilight 
shortest ? 

99. At Edinburgh,on what days is the twilight 
shortest ? 

100. At Madras, how long does twilight con- 
tinue when it is shortest ? 



* The solution of this question has caused more trou- 
ble to mathematicians than almost any other ; it has 
consequently been proposed and answered various times, 
in thti principal periodica) mathematical publications, 
with the hope of obtaining a pure spherical solution, as 
most of the gentlemen who have analysed it, have had 
recourse to jftixions, and therefore their investigations 
have been unintelligible to young mathematicians. "This 
is the first book in which the question was ever solved by 
the globe, and were it not that it is quite foreign to 
the design of the present treatise, the author would 
cheerfuliy investigate the problem, and show on what 
principles he has obtained his rule. 



132 PROBLEMS PERFORMED Btf 

101 . At Paris, how long does twilight continue 
when it is shortest ? 

102. At New Orleans, what is the length of 
twilight, when it is shortest ? 



PROBLEM XIX. 

By knowing the time when a Lunar Eclipse wilt 
happenjo tell the Places where it will be visible. 

Rules — 1. Find the place to which the Sua 
is vertical at the given time, by Problem XL 

2. Then as the Sun is visible to all the places 
above the horizon, so the Moon, being in opposi- 
tion to the Sun, at the time of her being eclipsed, 
is visible to all the places below the horizon,and 
consequently will appear eclipsed to all those 
places. 

EXAMPLES. 

On February 6th, 1822, at 5f hours A. M- 
there was an eclipse of the Moon ; where was 
it visible ? 

Ans. In the whole of North and South Amer- 
ica, and to the eastern coast of Africa ? 

103. On January, 6th, 1824,* s at9 hours A.M. 
the Moon will be eclipsed ; where will it be visi- 
ble ? 

104. On June 22d, 1880, at 2 hours P. M. the 
moon will be eclipsed ; where will it be visible ? 

105. On March 9th, 1830, at 2 hours P. H, 



THE TERRESTRIAL GLOBE. 133 

the Moon will be eclipsed ; where will it be vis- 
ible? 

106. June 8th, 1918, at 11^ hours P. M. the 
Moon will be eclipsed; where will it be visible ? 

PROBLEM XX. 

By knowing the time when a Solar Eclipse will 
happen, to find the Places on the Earth where 
it will be visible. 

Rule.— Find where the sun is vertical (by 
Prob XL) at the given hour; and bring the place 
to the zenith ; the eclipse, if a considerable one y 
will be visible to most of the places above the 
horizon. 

EXAMPLES. 

On March 4th, 1824, at 6 hrs. A. M. there 
will be an eclipse of the Sun ; where will it be 
visible ? 

Arts. It will be visible to the whole of Asia ; 
!New Holland ; to the greater portion of Africa ; 
the northern parts of Europe, as Russia, Siberia^ 
to the Great Southern and Indian Oceans, &c. 

107. On May 15th, 1836, at 2| hrs. P. M, 
there will be au eclipse of the Sun ; where will it 
be visible ? 

108. On November 29th, 1826, at \\\ hours 
A. M. there will be au eclipse of the Sun; where 
will it be visible ? 

J2 



134 THE CELESTIAL GLOBE. 

109. On March 4th, 1840, at 4 hrs. A. M. 
there will be ao eclipse of the Sua ; where will 
it be visible ? 



THE CELESTIAL GLOBE. 

A Description of the various parts of and the 
lines drawn on, the Celestial Globe* 

293. The Celestial Globe is a sphere, designed 
to ^present the appearance of the heavens ; the 
fixed "^irs being depicted thereon; according to 
their apparent magnitudes, and their situations 
with respect to each other. 

294. The constellations into which astronomers 
have so fancifully divided the stars are di- 
vided one from another by dotted lines, painted 
green upon some globes ; and upon others, the 
stars are nearly eclipsed by the creatures them- 
selves being figured thereon. 

295. The celestial globe, by turning on its ax- 
is, represents the apparent motion of the stars 
from east to west. 

296. The ecliptic is not only drawn and di- 
vided, as on the other globe, but the months, and 
days the Sun is in any particular sign, are written 
underneath in Latin. 

297. On each side of the ecliptic are drawn 
parallel circles thereto, extending 8° on each 



THE CELESTIAL GLOBE. 135 

side : this distance of 1 6° constitutes the zodiac, 
the sphere in which all the planets move. 

298. The arctic and antarctic circles are 
drawn in the same manner as they are on the oth- 
er globe, as are the tropical circles. 

299. The poles of the ecliptic are in the polar 
circles; the poles in which the hour-circles are 
fixed are the poles of the equator ; and the zenith 
and nadir are the poles of the horizon. 

300. The meridians on this globe are all 
drawn through the poles of the ecliptic, in the 
same manner as the meridians on the terrestrial 
globe are drawn through the poles of the equa- 
tor. 

301. There are two great circles drawn 
through the poles of the equator ; one passing 
through the first degree of 4ries and Libra, call- 
ed the Equinoctial Colure; and the other through 
the first degree of Cancer and Capricorn, called 
the Solstitial Colure. 

302. The parallels of latitude, are all drawn 
parallel to the ecliptic, in the same manner as 
they are drawn parallel to the equator on the ter- 
restrial globe. 

303. The wooden horizon, brazen meridian, 
hour-circles, and quadrant, are similar on both 
globes. 

DEFINITIONS. 

304. The latitude of either of the heavenly 
bodies is its Dearest distance to the ecliptic, and 
is north or south; in the same manner as the lati* 



136 PROBLEMS PERFORMED BY 

tude of any place on the earth, is its nearest 
distance to the equator. 

305. The longitude of either of the celestial 
bodies, is its nearest distance from the first de- 
gree of Aries, reckoned on the ecliptic. The lon- 
gitude of the sun, is the distance of the sun's 
place in the ecl<ptic,from the first degree of Aries. 

306. The declination of the stars or planets, is 
their nearest distance from the equinoctial. 

Obs. — The decli nation of a star on the celestial,is the 
same as the latitude of a place on the terrestial; and the 
right ascension of a star or planet, on the celestial, the 
same as the longitude of a place on the terrestrial globe. 

PROBLEM XXL 

To find the Right Ascension and Deelination of 
the Sun, the Stars, or Planets. 

Rule. — Bring the Sun, the planet's place, 
(found by Problem VII. Planetary Problems), or 
the given star, to that part of the brass meridian, 
numbered from the equator towards the poles ; 
the degree on the meridian is the declination,and 
the number of degrees between the brass merid- 
ian, and the first degree of Aries, is the right as- 
cension. 

What are the right ascension aud declination 
of a Lyra, ve! Vega ? 

4ns. Declination 38£° N. and right ascension 
277£°. 

Required the right ascension of Jupiter, April 
25th, 1824 ? 



!THE CELESTIAL GLOBE. 137 

Solution. — Jupiter's longitude by Problem 
VII. Astronomical Problems, will be 106°, or 
3 5 . 16%and his right ascension by the globe 107^° 
oearly. 

110. What is the right ascension of the Sun, 
Jan. 11th, Aug. 4th, Sept. 9^h, and Nov. 16ih ? 

111. What are the right ascensions and dedi- 
cations of the following stars ? 



Strius 


Markab 


Cor Hydra 


Algenib 


Spica Virginis 


Arietis 


Deneb 


Beteigeux 


Arcturus 


a Lepus 


Mar sic 


Regulus 


Ras \thagus 


Venae miatrix 


y Delphiaus 


Alphacca. 



112. What are the right ascensions of Venus, 
the Earth, Mars, Jupiter, and Saturn, on Nov. 
16th, 1823 ? 

PROBLEM XXII. 

To find the Latitude and Longitude of any of 
the heavenly Bodies. 

Rule. — Bring the pole of the ecliptic immed- 
iately under the brass meridian ; fix the quadrant 
over the pole of the ecliptic which is of the same 
name as the latitude of the star is; bring the edge 
of the quadrant over the given star ; the number 
on the quadrant against the star, is its latitude, 
and the number of degrees on the ecliptic, inter- 
sected by the quadrant, counting from the first 
point of Aries, is its longitude, 

12* 



138 PROBLEMS PERFORMED Wl 



EXAMPLES 



What are the latitude and longitude of Arc 



turus ? 



r J 



Ans. Latitude 31° N. and longitude 6 s 21^. 
113. What are the latitudes and longitudes of 



the following stars ? 




Cor Caroli 


Kochab 


a Andromeda 


Alkes 


Scheat Alperas 


Mira 


Arided 


Ancha 


Alderarain 


Situla 


AHoth 


Allair 


Dubhe 


Zubenna Krabbi. 



PROBLEM XXIIJ. 

Having the right Ascension and Declination of 
a Star, or Planet given, to find its Place on 
the Globe. 

Rule. — Bring the given decree of right as- 
cension on the equator to the brass meridian, and 
under the given declination, on the brass merid- 
ian, will be the star, or planet's place. 

EXAMPLES. 

What star is that whose declination is 12° 56' 
K. and right ascension 149° 25' ? 
Ans. Regulus# 



THE CELESTIAL GLOBE, 



139 



114. What stars have the following declina- 
tions and right ascensions ? 



Dee. 


Rt- Asc. 


Dec. 


i&. ^6C. 


o % 


o f 


o / 


o ' 


15 44 N 


174 42 


8 27 S. 


76 14 : 


16 5 N. 


66 6 


23 29 N. 


53 54 


8 27 S. 


76 9 


9 34 S. 


46 32 


45 47 N. 


75 29 


19 50 N. 


25 54 


7 21 N. 


86 5 


59 38 INT. 


11 11 


16 26 S. 


99 5 


55 26 N. 


7 19 



115. On July 19th, 1824, the right ascen 
sions and declinations of the planets are as folows : 
find their places on the globe. 
Mercury's right ascen. 110f° declin. 23 N. 
Venus' right ascen. 116° dec. 22° N. Mars' right 
ascen. 197|°, declin. 8° S- Jupiter's right ascen. 
115^° dec. 21 1' IN" Saturn's right ascen. 63° dec. 
19i°N. Herschell's right ascen. 284|° dec 231° S. 

PROBLEMX XIV. 
The Latitude and Longitude of a Star, or Planet 

being given, to find its Place on the Globe. 

Rule. — Bring the pole of the ecliptic to the 
brass meridian, and fix the quadrant over it , 
bring the longitude on the ecliptic to the edge of 
the quadrant, and under the given latitude ou 
the graduated ei\^e thereof, you will have the 
star, or planet's place. 



EXAMPLES. 

What star is that whose latitude is 0° 28' 
d longitude 4 J 26 e 57' ? 
Ans. Regulus. 



N. 



140 



TOCBLEMS PERFORMED BY 



1 1 6. What stars have the following latitudes 

and longitudes ? 



Lat. 


Long 


Lat. 


Long. 

s ■ i 


o ' 


s o / 


o t 


25 41 N. 


11 25 


29 18 N. 


9 28 51 


12 35 N. 


6 16 


61 44 JST. 


9 12 26 


59 55 N. 


11 2 29 


4 33 S. 


8 6 52 


21 6 S. 


11 57 


44 21 N. 


7 9 22 


26 43 INT. 


9 29 33 


30 52 N. 


6 21 ?? J 




117. On Sept. 1. 1824, the geoceutric longi- 
tudes and latitudes of the planets are as follows : 
find 
& 

lat. _ 

S. Jupiter's long, 4 s 3° 2 f , lat. 0° 21' N. Saturn's 
long. 2 s 7° 33', lat. 1° 58' S. Herschell's long. 9 s 
11° 57', lat. 0°25'S. 

PROBLEM XXV. 

To find the Time any Star, or Planet rises, sets, 
or comes to the Meridian, on any given Bay, 
at a given Place* 

Rules — 1. Rectify the globe for the latitude, 
and bring the given day on the ecliptic, and 12 
on the hour circle, to the brass meridian. 

2. Bring the given star, (or the planet's place, 
for a planet,) to the eastern ed^e of the horizon, 
and the hour on the hour-circle, cut by the brass 
meridian, will be the hour it rises ; bring it to 
the western edge,and the hour-circle will show 
the time it sets ; bring it to the meridian, and 
the hour-circle will show the time it culminates'; 



THE CELESTIAL GLOBE. 141 



EXAMPLES. 



At what hour will Arcturus rise at London, 
July 18th ? ^ 

Ans. 10 his. P. M. 

At what time will Jupiter rise, culminate, and 
set at London, July 3], 1824 ? 

The days from Jan. 1, to July 31, are 213, 
and 213x.0831=17° 43', and 96° 22'+ 17° 43' 
=1 ) 4° 5', and Jupiter's latitude, by N. Almanac 
is 0° 21' N. Therefore Jupiter will rise at 3 hr&. 
A. M. culminate at 11 hrs. A. M. and set at 7 
fars, R M. 

118. At what time will Sirius rise, culminate, 
and set, August 7, at Plymouth ? 

119. it what time will Rigel rise, culminate, 
and set, Nov 4, at Oporto ? 

120 At what time will Saturn rise, culminate, 
and set, at Madrid, Nov. 11, 1824 ? 

121. At what time will Venus rise, Nov. 7, 
1823 ? 

122. Will Venus rise before or after the Sun, 
September 16, 1825 ? 

123. What time will Sirius rise at Plymouth, 
March 4th ? 

124. What stars are on the meridian when 
Arcturus is rising, Nov. 6th, at Calcutta ? 

125. When Mars is on the meridian, Nov. 
16th, 1827: what stars are rising and setting ? 

126 What hour does Jupiter culminate the 
meridian of Paris, Sep. 16th, 1829 ; and what 
stars are rising and setting then ? 
127. When Procyon is culminating at London* 



142 PROBLEMS PERFORMED BY 

Sept. 11th, 1826, in what part of the heavens 
must I look for Mars ? 

128. What hour will Jupiter come to the me- 
ridian of Madras, on July 1.1th, 1824 ? 

129. What stars are never below the horizon 
of Plymouth ? 

130. What time will Venus come to the meri- 
dian of Philadelphia, on Feb. 7th, 1833 ? 

131. When the Pleiades are risiog at London, 
Nov. 6th, what stars are setting ? 

PROBLEM XXVI. 

The Latitude, Day. and Hour being' given, t& 
Jind what Stars are rising, setting, and culmi- 
nating. 

Rules — 1. Elevate the pole to the latitude, 
bring the given day on the ecliptic, and 12 on 
the hour-circle to the brass meridian. 

2. Turn the glebe until the given hour is un- 
der the brass meridian : then the stars on the 
eastern ed^e of the horizon are rising, those on 
the western edge are setting, and those under the 
meridian are culminating. 

EXAMPLES. 

At 9hrs. P. M. Dec. 4th, at Londeu, what 
stars are rising, setting, and culminating ? 

Ans. Corona Borealis, AJtair, Varia, &c- are 
rising; Arietis s Almach,Cassiopeia. &c. are culmi- 
nating ; and Sirius, Cor Caroli, &c. are setting* 



THE CELESTIAL GLOBE. 143 

132. At 9 hrs- A- M. At Plymouth, Aug. 6th, 
what stars are rising, setting, and culminating ? 

133. What stars are rising, setting, and cul- 
minating, at the following places, at the following 
times ? 

Madras, Aug. 6th, 4| hrs. P. M. 
Paris, July 8th, 7 hrs. A. M. 
Petersburgh, JNTov. 9th, 6 hrs, P. M. 
Gibraltar, Feb. 11th, 1\ hrs. A. M. 
Corsica, Oct 16th, \\\ hrs- P. M. 
London, Bee, 13th, 9| hrs. A. M. 

134. Is Mars above or below the horizon c( 
York, June 13th, 7 hrs. A. M. 1823 ? 

135. fs Saturn visible at Madrid, April 11th, 
9 hrs. A. M. 1825? 

136. Is Jupiter above the horizon of Aber- 
deen, Nov. 17th, 1823, at 11 hrs. P. M. 



PROBLEM XXVII. 



To find the Azimuth and Altitude of any given 
Star, at any placemen a given Day and Hour. 

Rijles.— 1. Bring the given day on the eclip- 
tic, ami 12 im the hour-circle to the brass meri- 
dian, and elevfcte the pcie to the latitude. 

2. Fix the quadrant in the zenith, and turn 
the globe until the ^iven hour is under the me- 
ridian- 

3. Lay the graduated edge of the quadrant 
over the gives star ; the degree against it will be 
the star's altitude : and the degree against the 



144 PROBLEMS PERFORMED Bit 

quadrant, on the inner circle of the horizon* 
from the north or south, will be the star's azi- 
muth. 

EXAMPLES. 

What are the azimuth and altitude of Regulus 
at London, April 8th, 7 hrs. P. M. ? 

Ans- The altitude of Regulus is 42° ; and its 
azimuth N. 35 W. 

137. What are the azimuth and altitudes of 
the following stars, at the respective times and 
places ? 

Aldebaran, London, Aug. 7th, 4 hrs. A.M. 
Achernar, Cape- Horn, 'Nov. 1 1th, 8 A.M. 
Antares, Paris, April 6th, 4 A. Ma 

Sirius, Washington, Aug. 7 6h, 6| A.M. 

Spica Buda, t Sep. 19th, 10| A.M. 

Castor, Moscow, Jan. 11th, 6£ P.M. 
Capella, Pekin, April 26th. 11 P.M. 

Yega, Jeddo, July 17th, 10 P.M. 

PROBLEM XXVIII. 

To find the rising and setting Amplitudes, and 
Meridian Altitude of any Star or Planet at 
any Place on any Day. 

Rules — 1. Elevate the pole to the latitude, 
and turn the globe until the given star, or planet's 
place, comes to the eastern edge of the horizon, 
and the distance, on the inner circle of the hori- 
zon, from the point where the star, or planet in- 
tersects it to the east, is the rising amplitude ; 
and by bringing it to the western edge, and pro- 



THE CELESTIAL GLOBE. 145 

ceeding as before, you will obtain its setting am- 
plitude.* 

2. Bring the star to the meridian, and the dis» 
lance of the star from the horizon will be its me- 
ridian altitude. 

EXAMPLES. 

What are the rising and setting amplitudes of 
Arcturus at London, with its meridian altitude ? 

Ans. E. 34° S. its rising amplitude : W. 34° S. 
its setting amplitude ; and 58° its meridian alti- 
tude. 

What will be the rising and setting amplitudes 
of Jupiter, April 4th, 1824, with his meridian al- 
titude at New-York ? 

Solution. — Long, of Jupiter (by Prob. VII. 
Planetary Problems) 14° 1 3' oi Cancer; Jupiter's 
lat. by Nautical Almanac 0° 7' N. Then as this 
problem directs, the planet's rising amplitude will 
be found E. 30° N. ; setting amplitude W.30* 
N. ; aiicl its meridian altitude 72°. 

138. Required the rising and setting ampli- 
tudes, and meridian altitudes of the following 
stars at the respective places :■ 



Algol 


at 


Plymouth 


Rastaben 


— 


Petersburgh 


Alkes 


—- . 


Calcutta 


Canopus 


_ 


St. Helena 


Fomalhaut 


— . 


Madras 


CapeSla 


— i 


Plymouth 


Aiphacea 


— 


York. 



* When using the globe for a planet, its Tonsj. Sz lat. 
must be found by some Almanac, and a small mark for 
the planet's place, must be made on the globe with a 
soft lead pencil. 

13 



146 PROBLEMS PERFORMED BT 

139. How long will Arcturus rise after th£ 
Sun, on Nov. 16th, and what is the difference of 
their meridian altitudes, at London ? 

140. When Arcturus is setting on April 6th, 
at Paris, what stars are rising setting, and cul- 
minating ; and whether does Sirius rise before or 
after the Sun on that day ? 

141. What is the difference of the rising am- 
plitudes of Sirius and Aldebaran at Plymouth;, 
with the difference of their meridian altitudes ? 

142. When the Sun is setting, November 8tb 9 
at Madrid, what star is that which is rising, whose 
rising amplitude is E. 29° S. ; and what star is 
that whose altitude is 31°, and azimuth S.41° BJ 

PROBLEM XXIX. 

To determine whether Jupiter and Venus are 
morning or evening Stars, on any particular 
Day, at a given Place- 

Rules — 1. Find the longitude of the given 
planet, (by Problem VII. Planetary Problems,) 
and the longitude of the Sun* 

2- Then if the longitude of the Sun be less 
than the longitude of the planet, it will be to the 
east of the Sun, and will set after him in the eve- 
ning, consequently will be an evening star : but 
if the longitude of the Sun be greater than the 
longitude of the planet, it will be to the west of 
the Sun, and will rise before him in the morning, 
and will consequently be a morning star. 

Note. — The time the planet rises may be found by 
'Problem XXV. 



THE CELESTIAL GLOBE, 14.7 



EXAMPLES. 



Is Venus a morning or an evening star, oa 
May 1 8th, i 824 ? 

Solution. — The days from January 1st to May 
18th, are 139. Then 1.6021X139=222° 42', and, 
the long. Ja?.!. i, 150° 2' + 222° 4l'=373° 43'; 
therefore 373° 43', or 0* 13°43'is Venus' longi- 
tude ; the Sun's longitude May 18th, is h 27° 25* 
■which being greater, proves Venus to be a morn- 
ing star. 

143. Will Jupiter be a morning or evening 
star, August 17th, 1829? 

144. Will Venus be a morning or evening star, 
on November 29th, 1823 ? 

145. What time will the beautiful planet Venus* 
rise, August 16th, 1825 ? 

146 What time will Jupiter rise and set, April 
4th, 1824 ? 

147. Will the planet Venus appear in the eve- 
ning or morning of December 17th, 1823 ? 

148. What is the difference of longitude be- 
tween Jupiter and Venus on May 18th, 1824 :. 
and will either of them be visible in the even- 
ing s and what is the difference in the times of 
their culminating ? 

149 Will Saturn be above the horizon of 
Plymouth, September 13th, 1823, at 8 o'clock, 
P.'M. 



148 PROBLEMS PERFORMED ST 



PROBLEM XXX. 

Having the Sun or any Star's ruin? or setting 
Amplitude on any Day > to find ike Latitude of 
the Place. 

Rules — 1. Bring the Sun's place and 12 oq 
the hour-circle, to the brass meridian. 

2. Bring the Sun's place, or the given star, to 
the east, or west edg* of the horizon, according 
as the rising or setting amplitude is #iveu ; and 
elevate or depress iht pole, until the Sun's place, 
or given star, corresponds to the given amplitude: 
then, so many degrees as the pole is elevated, 
will the latitude of the required place be. 

EXAMPLES. 

What is the latitude of the place, where the 
Sun's rising amplitude is E. 26° N.on May 16th? 
Ans. 461° JNT. 

150. What is the latitude of the place, where 
the rising amplitude of Sirius is E. 29 S. ? 

151. Observed the Sun to rise Nov. 4th, E. 
23° S. in what latitude was T ? 

152. In what latitude will Rigel rise S. 68° E.? 

153. In what latitude is the Sun's setting am- 
plitude W. 17° S. on August 14th ? 

154. la what latitude will Procyon rise 
E.S.E. ? 



$HE CELESTIAL GLOBE. 14§/ 



PROELEM XXXI. 

slaving the Sun or any Stars Meridian Altitude 
given, to find the Latitude, 

Rules — 1. Bring the giveu day, on the 
ecliptic, or the given star, to the brass meri- 
dian. 

2 Elevate or depress the pole,until the given 
number of degrees is contained between the hori- 
zon and the Sun's place, or the given star ; the 
number of degrees the pole is elevated is the 
latitude required. 

EXAMPLES. 

The meridian altitude of Arcturus was 48°, 
-what was the latitude ? 
Am. 61°. 

155. Being af sea, I observed the Sun's me- 
ridian altitude on July 7th, to be 49^°; what was 
the latitude ? 

156. The observed meridian altitude of Sirius 
was 27° ; what was the latitude ? 

157. The altitude of Castor, when on the me- 
ridian, was 71° ; what was the latitude ? 

158. How far south must I go from Plymouth, 
to lose sight of Pollux? 

159. How many degrees south must a person 
travel from Petersburgh to lose sight of the north 
polar star ? 

13* 



130 PROBLEMS PERFORMED $^ 

PROBLEM XXXII. 



To find the Distance of any two Stars, one from 
another. 

Rule. — Lay the quadrant over the two stars, 
and the number of degrees betweea them, will be 
the distance required. 

EXAMPLES. 



How far distant is Rigel from Sirius ? 
Ans. 23°. 



1 60. What is the distance between the follow- 
ing stars ? 

Aldebaran and Castor 
Rigel aud Procyon 



Vega and AJtair 
Capella and Betelgeux 



Markab and Scheat 
Deoeb and kntares 
Arcturus & Fomalhaut 
Castor and Sirius. 



PROBLEM XXXIII. 



To find on what day any given Star passes a 
given Meridian, at a given Hour 

Rule. — Elevate the pole to the latitude; bring 
the given star ai?i the driven hour ou the houiy 
circle to the meridian; turn the globe until 12 at 
noon is on the meridian, the day ou the ecliutip 
tinder the brass meridian is the day required. 



THE CELESTIAL GLOBE* 151 



EXAMPLES 



On what day will Arcturus pass the meridian 
of London at 7 hrs. P. M. ? 
Aiis. August 1st. 

161. On what day will Sirms and the Sun be 
on the meridian of Bristol at the same tiaie ? 

162. On what day will Procyon pass the me- 
ridian of Madrid three hours after the Sun ? 

163. On what day will Aldebaran be on the 
meridian of Paris, 9 hrs, before the Sun ? 

164. On what day will Castor culminate 7hrs. 
before the Sun at Plymouth ? 

165. On what day will the Pleiades culminate 
at 4 hrs. P. M. at Madras ? 

PROBLEM XXXIV. 

On any given Day and Hour, at a given Place, 
to find the Angle which the Ecliptic makes with 
the Horizon, called the Nonagesimal Degree* 

Rules — 1. Elevate the pole to the latitude; 
bring the given day, and 12 on the hour-circle, 
to the brass meridian, and turn the globe until 
the given is under the meridian. 

2- From the point where the ecliptic intersects 
the horizon, observe the great circle which 
passes through the pole of the ecliptic, and note 
where the circle cuts the brass meridian ; the 
distance from that point to the zenith is the angl§ 



% 3£ mOBLEMS PEKFOEMED BY 

the ecliptic makes with the horizon, or the 
nonagesimal degree. 

EXAMPLES, 

166. What angle does the ecliptic make with 
the horizon, od July 6th, at 6 hrs. A. M. at Lon- 
don ? 

Arts- 44i°. 

167. What is the altitude of the nonagesimal 
degree at London, on June 21st, and Dec. 21st, 
at 11 hrs. A. M ? 

168. Find when the nonagesimal degree is the 
least at Paris. 

169. On what day will the altitude of the 
uonagesimal degree at Cambridge be a maxi- 
mum ? On this depends the determination of the 
shortest twilight. 

170. What angle does the ecliptic make with 
the horizou at Cambridge,on October 12th, 4hrs. 
43' A. M. ? 

PROBLEM XXXV. 

The Latitude of ike Place, Day, and Hour being 
given, to represent the Appearances of the 
Heavens, so as to tell the Name of any Har 
we may observe. 

Rule. — Elevate the pole to the latitude ; 
bring the given day on the ecliptic, and 1 2 on 
the hour-circle to the brass meridian ; turn the 



£HB CELESTIAL GLOBE, 153 

globe until the given hour is under the meridian: 
let the north pole be placed towards the north, 
and the eastern part of the globe to the east, the 
globe will then exactly represent the appearance 
of the heavens, and any star's name may be found 
by its situation with respect to other &tars. 

EXAMPLES* 

Represent the appearance of the heavens, at 
Plymouth, January 3d, 7 hrs. P. M. 

Soiutiori — Sinus has just risen : the beautiful 
constellation, Orion, is in the S. E.; the Pleiades, 
Aldebaran, are approaching to the meridian, ap- 
pearing to the north-west of Orion ; Arietis and 
Tiiangulum are on the meridian ; the grand 
geometrical formed by Scheet, Mzirkab, Algenib, 
and a Andromeda, the three former in Pegasus, 
and the latter in Andromeda, are in the south- 
west; the Dolphin, the Arrow, and the Hart,are 
Dearly in the horizon in the west. 

171, Represent the appearance of the heavens 
at New-York, July 7th, at 6 hrs. A. M. and tell 
me the principal stars visible. 




154 MOSLEMS MRFOBHEB BIT 



PROBLEM XXXVI. 

Tojind the Cosmical, Heliacal, and Achronical 
rising or setting of any Star ; or to find on 
what Day any Star will have such rising or 
setting. 

DEFINITIONS. 

1. When a star j Jg I at sun-rising,it j ™™l 
cosmically. 

2. When a star \ ns f s \ at scm-setting,it 

r SCIS \ 

achronically. 

The heliacal \ ™|?^ I of any star, is wheo 

it first appears in the morning, or disappears in 
the evening, after having been immergerf in the 
sun's rays. 

Note* — Stars of the first magnitude appear when the 
sun is 12° below the horizon ; second magnitude*, 13° 5 
third magnitude, 14? ; fourth magnitude, "15°, &c. 

Rules — 1, Elevate the pole to the latitude ; 
screw the quadrant hi the zenith, and bring the 
given day on the ecliptic to the eastern edge of 
the horizon, and the stars there are rising cos- 
mically ; those on the western edge are setting 
cosmically. 

2. If the day be required when any star rises 
6x. sets cosniically, after the globe is elevated to 



THE CELESTIAL GLOBE. 15£ 

the latitude, bring the star to the eastern edge 
for the cosmical rising, and to the western edge 
for the cosmical setting, the day on the ecliptic^ 
cut by the horizon, will be the day required. 

For the Achrmical rising or setting, 

Bring the given day on the ecliptic to the west- 
ern edge of the horizon, those on the eastern are 
rising achrouically, those on the western are set- 
ting achronically. 

For the Heliacal rising and setting. 

Bring the given day on the ecliptic to touch 
12° below the eastern or western edge of the 
horizon respectively for the rising or setting,thea 
the stars of the first magnitude, on the western 
or eastern part of the horizon, are rising or set- 
ting heliacally ; by using 13°, 14°, and 15°, in- 
stead of 12°, you have the stars of the second* 
third, and fourth magnitudes,, which respectively 
rise and set heliacally. 

EXAMPLES; 

What stars rise and set cosmically, achronical* 
]y, and heliacally, at London, July 8th ? 

Solution. — Betelgeux rises cosmically; Miracb 
sets cosmically ; Scheat and Enir rise achron- 
ically ; Cor Hydra sets achronically; Fomaihaut 
rises heliacally ; and Spica Virginia &c* se& 
heliacally. 



lv»6 PROBLEMS PERFORMED BX 

1 72. On what day at London will Arcturim 
rise cosmically ? 

173. On what day at Madrid will Sirius rise 
achronically ? 

174. What stars set heliacally at York, Au- 
gust 7th ? 

175. When will Aldebaran rise at snn-rising, 
at Bristol ? 

176. When will Castor set cosmically at Par- 
is ? 

177. When will the Pleiades set at sun rising* 
at Plymouth ? 

178. What stars rise achronically at Peters- 
burgh, August 17th ? 

179. What stars set heliacally, at Madras, 
November 1 3th ? 

180. Hesiod, a celebrated Grecian poet, says, 
that at Ascra, lat. 38° N as the Sun entered Pis- 
ces, Arcturus rose achronically: how many years 
ago did he live, supposing the precision of the 
equinoxes to be 50 J seconds in a year ? 

181. When in the year 1823, will Jupiter, 
Mars, and Venus respectively rise at sun-setting, 
at Plymouth ? 

182. When will Herschell in the year 1824 
rise at sun rising, at Madrid ? 

183. When, in the year 1823, will Jupiter rise 
and set cosmically, at London ? 

184. When in the year 1823, will Mars be on 
the meridian at midnight, at London ? 



157 
SUPLEMENTARY CHAPTERS, 



CHAP. I. 

XHE NATURE OF THE PLANETARY REVOLUTIONS, 

The Sun is in the centre of the Solar system, 
and the Planets harmoniously revolve around it, 
constantly describing the same curve, which 
curve is an ellipse, though approaching very 
nearly to a circle. 

This truth has been most fully demonstrated 
by the most eminent philosophers and mathema- 
ticians ; and though in the infancy of astronomy, 
various systems were propagated by different 
astronomers to account for the various phenom- 
ena of the Heavenly bodies, the most remarka- 
ble of which systems were those of Ptolemy and 
Tycho Brahe, each of whom imagined the Sua 
and planets to revolve around the Earth, yet 
the present system now called the Solar, Coper- 
nican, or Newtonian system, which naturally 
arose from the errors of the others, has been sa 
beautifully illustrated, and clearly demonstrated 
by its reviver, Sir Isaac Newton and other math- 
ematicians, that it must gain the assent of all who 
understand its nature. It would be impossible, 
within the limits of a treatise like the present, to 
give the various demonstrations of that or other 
astronomers at any length; but as it may be ne- 
cessary for the young student, both to confirm 
him in the truths found in the former parts 
of this volume, for his more clearly beholding 
the harmony and sublimity of the noblest of 
Sciences, and at the same time to direct his at- 
tention to the wisdom and goodness of his 



15S THE NATURE OF 

Maker, we shall very briefly, though clearly 
show, that the Solar is the true system of the 
universe. It is a known principle in the laws 
of motion, that if any body revolve around a- 
nother as its centre, it is necessary that the cen- 
tral body be always in the plane in which the re- 
volving body moves : (Emerson's Astronomy:) 
and therefore, if the Sun move round the Earth 
in a day, its diurnal path must always describe 
a circle whose plane must divide the Earth into 
two equal hemispheres : to every portion of the 
Earth the Sun would always rise in the same 
part of the Heavens, that is, it would at any 
particular place on the Earth always have the 
same rising and setting amplitude, (vide art.290.) 
it would always rise due east and set due west, 
it would always have the same position, be on 
the same point of the compass, or have the same 
azimuth, at the same time every day; it would 
every day in the year have the same meridian 
altitude ; the day would always be equal to the 
night, each equal to twelve hours : the Sun 
"would, to every portion of the Earth preserve 
that regular uniformity it does now at the equa- 
tor, constantly rising and setting at six o'clock. 
The meridian altitude of the Sun would always 
be proportionable to the inclination of the axis 
of the Earth, if the axis were perpendicular to 
the plane of the Earth and Sun's centre ; every 
portion of the Earth would every day of tlie 
year invariably and uniformly receive the in- 
vigorating influence of the refulgent rays of the 
revolving orb, and at the Poles, the Sun would 
appear always in the horizon : if, on the con- 
trary, the Poles of the Earth were parallel to 



THB FLANETAftY REVOLUTIONS. 15& 

the plane of the Earth and Sun's centre, the Sun 
would illuminate both the poles constantly on 
the same day, and appear in their zenith ; and 
indeed, if the axis of the Earth were inclined in 
any direction whatever, every portion of the 
Earth would every day receive the rays of the 
Sun, and be enlightened by its refulgence ; but 
since the Sun appears to rise in different parts 
of the horizon, that is, its rising amplitudes are 
different every day ; that its azimuth is different 
at the same time on different days ; that its me- 
ridian altitude is greater or lesser every day ; 
that it does not rise every day at the same time; 
that it does not rise and set every day at sis 
o'clock ; and that the frigid zones of the Earth 
do not every day in the year receive the rays of 
the Sun ; the Sun caunot revolve around the 
Earth, and the Earth consequently has a rota- 
tion on its axis to produce the apparent revolu- 
tion of the Sun. If the Sun were to revolve 
around the Earth once in twenty-four hours, as 
it constantly must describe the same curve, and 
as the Sun must rise and set at the same time 
every day, there could be no variety of seasons; 
for, as the seasons are occasioned by the variety 
in the lengths of the day, and as the length of 
days must constantly be equal, so there could 
be no different seasons ; here then we may dis- 
cover the wisdom and kindness of our heavenly- 
Father. The Planets also, if they revolved 
around the Earth as a centre, would invariably 
rise and set at the same time, attain to the same 
meridian altitude every day, and would appear 
to move regularly round in their respective 
orbits ; but as they do not appear to move with 



160 THE NATURE Of 

regularity and uniformity, as sometimes they ap= 
pear to remain fixed among that host, that innu- 
merable multitude of stars which in every direc- 
tion encircle the firmament , at other seasons 
they appear to revolve with a greater or with 
a lesser velocity, describing different portions 
of their orbits in the same time, and frequently 
appear to move retrograde or contrary to the 
order of the Zodiac ; they cannot revolve around 
the Earth as a centre, and these appearances 
can only be accounted for by the revolutions of 
the Planets, among which is the Earth, harmoni- 
iously and regularly revolving around the Sun : 
but the young astronomer may say, why does 
uot the Moon, which you have said revolves a- 
round the Earth, always rise and set at the same 
time, attain to the same meridian altilude,&c.&c. 
every day ? These differences in the times of 
rising, setting, &c. &c. are occasioned by a com- 
position of motions, one in the Earth, and anoth- 
er in the Moon, for while the M^on is proceed- 
ing in her orbit around the Earth, the Earth is 
proceeding in its orbit around the Sun ; and the 
difference in their motions, or more philosophical- 
ly, |the difference of their daily lougitudes, is the 
portion the Moon has to advance in her orbit,later 
on one day than on a preceding ; and so long as 
the Earth takes to describe that portion of a 
great circle, so long will the Moon rise later each 
evening, which is about three quarters of ae 
hour. To exemplify this. At new moon, the 
Sun, Moon, and Earth are in the same straight 
line, the Moon being in the middle ; then as 
the Moon's orbit is situated nearly in the plane 
of the ecliptic, these bodies rise, attain the me- 
ridian, and set at the same time, consequently, 



THE PLANETARY REVOLUTIONS. 161 

the Moon is hidden, as her darkened hemisphere 
is towards the Earth; but on the second day from 
her conjunction, she has traversed -* ¥ th part of 
her orbit (as she revolves around the Earth in 
about 30 days) = 12°, and as the Earth has re- 
volved only 1° in that time, the Moon is then 11^ 
to the east of the Sun, then she adorns our west- 
ern sky in the evening ; so that she rises, as has 
before been observed,as much later every day as 
the Earth is describing an arc of 11°; so when 
the Mooq comes in opposition to the Hun and the 
Earth is directly in a line between these lu- 
minaries, the moon rises in the eastern the mo- 
ment the Sun sets in the western horizon ; the 
Moon comes to the meridian at midnight, as the 
Sun does at midday. Another reason why the 
Moon does not uniformly describe the same arc, 
is, that her orbit is constantly varying ; she, un- 
like all the planets, goes round her primary in 
a different curve every revolution ; the places of 
her nodes are continually varying, while the ap- 
ses of the Earth, and the nodes of the planets, 
remain unalterably fixed ; and were it not for 
these reasons,uamely,the combinations of the mo- 
tions of the Earth and Moon, and the difference 
of her orbicular curve, she would present those 
appearances to us which the Sun would, if he 
revolved around us, and the same as the fixed 
Stars actually do present ; constantly and daily 
having the same meridian altitudes, the same 
rising and setting amplitudes ; describing the 
game arc in the heavens, &c. &c. all oi which 
phenomena are produced by the rotation of the 
]3arth on its axis. 

14* 



162 
CHAP. II, 

THE CAUSES OF PLANETARY MOTION, 

8nt Isaac Newton was the first who attempted 
to give a physical account of the motions of the 
Planets, which should accommodate itself to all 
the irregularities which astronomers had ever ob- 
served in their motions. 

He demonstrated, that if the Planets were sup- 
posed to gravitate towards the Sun, and to one 
another, and at the same time to have a projec- 
ting force originally impressed upon them, the 
primary ones might all describe ellipses around 
that luminary, which would be in one of the foci 
of such elliptic orbit. The secondary planets 
might also describe ellipses about their respective 
primaries, without being disturbed by the contin- 
ual motion of the centres of their revolution. This 
principle of gravitation is an inherent principle, 
or mutual affection in all kinds of matter, in or- 
der to their uniting and coalescing into a globu- 
lar form, for their better preservation. 

This principle of gravity is very frequently 
called the attraction of gravity, and the centri- 
petal force, and it is one of the most universal 
principles in nature. We see and feel it operate 
on all bodies near the Earth ; it is by this opera- 
tive power, this inherent principle, that a stone 
or heavy body projected in the atmosphere is 
compelled to descend to the Earth again ; it is 
by this power that a body thrown from the top 
of an edifice, immediately is drawn towards the 
centre of attraction ; it is by this power that the 
planets, the satellites,and very probably the Sun, 



THE CAUSES OF PLANETARY MOTION, 163 

with all his attending planets, satellites, and com- 
ets, revolve constantly around their centre of 
gravity. 

One very essential property of gravity is, 
that its attractive force is always equal to the 
quantity of matter in any body, and from the 
natural affinity which one particle of matter has 
to another, arises all the motion, and consequent- 
ly all the mutation in the universe. By this, 
heavy bodies descend, and light ones ascend ; by 
this, projectiles are directed, vapours and exha- 
lations rise, rains descend, rivers glide, tides ebb 
and flow, the air presses, the planets revolve, 
comets proceed, and all the machinery of nature 
is in constant and majestic motion ; it connects it- 
self with us in all our peregrinations, our bodies 
as well as the planets are its subjects, and it is 
by this that our antipodes can stand with their 
feet directed to the centre of the Earth, and con- 
sequently against ours. The projectile or cen- 
trifugal force, is that force by which the planets 
are affected, and which prevents their falling in- 
to the centre of gravity of the solar system : 
this force acts perpendicularly to the centripetal 
force, and preserves the planets in their orbits . 
and it is by the combination of these forces, that 
the whole universe is regulated- 



164 
CHAP. III. 

THE MILKY WAY. 

The Milky Way, or via lactea, is (says Dr. 
Herschel) a most extensive stratum of stars of 
various sizes, and our Sun (with all its planets, 
satellites, and comets) is one of the heavenly bo- 
dies belonging to it : that eminent astronomer 
says, he viewed this shining zone in almost eve- 
ry direction, and found it composed of shining 
stars, whose number constantly increases or de- 
creases according to its apparent brightness to 
the naked eye. But, says he, in order to dev el- 
ope the ideas of the universe that have been sug- 
gested by my late observations, it will be best to 
take the subject from a point of view, at a con- 
siderable distance both of space and time. The 
laws of gravitation, which no doubt extend to the 
remotest regions of the fixed stars, will operate in 
such a manner, as most probably to produce the 
following remarkable effects : 

1st. It will frequently happen that a star, be- 
ing considerably larger than its neighbouring 
ones, will attract them more than they will be at- 
tracted by others that are immediately around 
them ; by which they will be, in time, as it were, 
condensed about a centre ; or, in other words, 
form themselves into a cluster of stars,of almost a 
globular form, more or less regularly so, accord- 
ing to the size and original distance of the sur- 
rounding stars. This cluster of Stars is called 
a Nebula. 

2d. The next case, which will happen almost 
as frequently as the former, is, where a few stars, 



THE MILKY WAT, 165 

though not superior in size to the rest, may- 
chance te be rather nearer each other than the 
surrounding ones, for here also will be formed a 
prevailing attraction in the combined centre of 
gravity of them all, which will occasion the 
neighbouring stars to draw together ; not, indeed, 
?o as to form a regular globular figure, but, how- 
ever, in such a manner as to be condensed to- 
wards the common centre of gravity of the whole 
irregular cluster. And this construction admits 
of the utmost variety of shapes, according to the 
number and situation of the stars which first give 
rise to the condensation of the rest. 

5d. From the composition and repeated con- 
junction of both the foregoing forms, a third 
may be derived : when most large stars, or com- 
bined small ones, are situated in long extended, 
regular, or crooked rows, hooks or branches ; 
for they will also draw the surrounding ones so 
as to produce figures of condensed stars coarsely 
similar to the former. 

4th. We may likewise adroit of still more ex- 
tensive combinations ; when, at the same time, 
that a cluster of stars is forming in one part of 
space, there may be another collecting in a dif- 
ferent, but, perhaps, not in a far distant quarter, 
which may occasion a mutual approach towards 
their common centre of gravity. 

5th. From this theorectical view of the heav- 
ens, which has been taken from a point not less 
distant in time than in space, we will now retreat 
to our own retired station, in one of the planets 
attending a star in its great combination with 
numberless others : and, in order to invests 



i«a 



THE MILKY WAY. 



gate what will be the appearances from the con- 
tracted situation, let us begin with the naked 
eye. The stars of the first magnitude being, in 
all probability, the nearest, will furnish us with 
a step to begin our scale. Setting off, therefore, 
ivith the distance of Sirius, or Arc turns, for in- 
stance, as unity, we will at present suppose, that 
those of the second magnitude art at doub!e,those 
of the third, treble the distance, &c — Taking it 
for granted then, that a star of the seventh magni- 
tude (the smallest supposed visible to the 
naked eye) is about seven imes as> far as one of 
the first ; that au observer, who is enclosed in a 
globular cluster of stars, and not far from the 
centre, will never be able with the naked eye to 
see to the end of it, for since according to the 
above estimations he can only extend his views 
to about seven times the distance of Sirius,it can- 
not be expected that his eyes should reach the 
borders of a cluster, which has, perhaps, not less 
than fifty stars in depth every way around him. 
The whole universe to him, therefore, will be 
comprised in a set of constellations, r.chlv orna- 
mented with scattered stars of all sizes. Or, if 
the united brightness of a neighbouring cluster of 
sturs should, to a remarkably clear night, reach 
his sight, it will put on the appearance of a small, 
feint, whit»sh, nebulous cloud, not to be perceiv- 
ed hut with the greatest attention. Let us sup- 
pose him placed in a much extended stratum, or 
branching cluster of millions of stars,such as may 
fall under the third order of nebula already uo- 
ticed; here also the heavens will not only be rich- 
ly scattered over with brilliant constellations, but 
a shining zone, or milky way, will be perceived 



THE MILKY WATT. 16? 

to surround the whole sphere of the heavens^ 
owing to the combined light of those stars which 
are too small, that is, too remote, to be seen. Our 
observer's sight will be so confined, that he will 
imagine this single collection of stars, though he 
does not perceive even the thousandth part of 
them, to be the whole contents of the Heavens. 
Allowing him now the use of a common teles- 
cope, he begins to suspect that all the milkiness 
of the bright path which surrounds the sphere 
may be owing to stars. He perceives a few 
clusters of them in various parts of the heavens, 
and finds, also, that there are a kind of nebulous 
patches ; but still his views are not extended to 
reach so far as to the end of the stratum in 
which he is situated ; so that he looks upon these 
patches as belonging to that system which to 
him seems to comprehend every celestial object. 
He now increases his power of vision ; and, ap- 
plying himself to a closer observation, finds that 
the Milky Way is indeed no other than a collec- 
tion of very small stars. He perceives that 
those objects which had been called nebulce 9 
are evidently nothing but clusters of stars ; their 
number increases upon him, and when he re- 
solves one nebula into stars, he discovers ten 
new ones which he cannot resolve : he then 
forms the idea of immense strata of fixejl stars, 
or clusters of stars, and of nebulae ; still going on 
with such interesting observations, he now per- 
ceives that all these appearances must naturally 
arise from the confined situation in which he 
is placed. Though the words condensation, 
cluster, &c. of stars, frequently occur, we are 
(says the eminent Mr. Vince,) in no w r ay to ima= 



IBB TME MILKY WAt* 

gine that any of the celestial bodies in our ne« 
bula are nearer to one another than we are to 
Sirius, whose distance is supposed to be not less 
than 400,000 times the distance of the Sun from 
us, or thirty-eight millions of millions of miles. 
The whole extent of the nebula being in some 
places near 500 times as great, must be such that 
the light of a star placed at its extreme boundary, 
supposing it to fly with the velocity of twelve 
millions of miles every minute, must have takeu 
near 3000 years to reach us I whence Young, ia 
his Wight Thoughts, sayfc, 

" How distant some ®f the nocturnal suns ! 
So distant, says the sage, 'twere not absurd 
To doubt, if beams, set out at Nature's birth, 
Are yet arriv'd at this our foreign world ; 
Yet nothing half so rapid as their flight." 

" Every star then may be considered as the 
centre of some magnificent system, irradiated by 
its beams, and revolving about it by its influence. 
ThiiSjthe empire of God is magnified, his power 9 
wisdom, and goodness made manifest. He is not 
glorified in one Earth, or in one system of worlds 9 
but in an indefinite number. — Could we dart to 
the loftiest apparent star, we should there see o- 
ther skies expanded, other suns distributing their 
inexhaustible beams of day ; other stars decora- 
ting the hours of night; and other systems estab- 
lished in unknown profusion through the bound- 
less dimensions of space, and even there we shall 
be only advanced to the suburbs of the creation 
the frontiers of the great Creator's kingdom " 



VOCABULARY 



OF 



Astronomical Terms? 

STARS' NAMES, &c. &c. 

AS THEY ARE USUALLY ACCENTED, 



Ache'rnar, a star of the first magnitude in Eridanus* 

Acro'nical, a term applied to any heavenly body when 
it is in opposition to the sun. 

Acu'bens, a star marked a in Cancer, 

Aldera'men, a star marked a in Cepheus. 

A'dhil, a star of the sixth magnitude in Andromeda, 

Alde'baran, a star of the first magnitude in Taurus. 

Aldha'fera, a star of the third magnitude in Leo. 

A'lgenib, a star of the second magnitude in Perseus* 

A'lgol, a star of the second magnitude in Perseus. 

Algorab,a star of the third magnitude in Corvus. 

Alkes, a star of the third magnitude in Crater et Hydra^ 

Alioth, a star of the third magnitude in Ursa Major. 

Alrnaca'ntars, are circles of altitude, parallel to the ho- 
rizon. 

A'imaael^a star of the second magnitude in Andromeda, 

Alphe'ratz, a star of the second magnitude in Androm- 
eda. 

A'ltitude, the altitude of any celestial body is its nearest 
distance to the horizon. 

15 



170 A VOCABULARY OB 

Alru'ceabah, the pole star ; a star of the third magnitude 

in Ursa Minor. 
Amphiscii, are the people who live in the torrid zone. 
A'mpiitude, is the point of the horizon at which a foody 

rises from the east, and sets from the west* 
Anale'rama, is a projection of the sphere on the plane 

of the meridian* 
A'ngha, a star of the third magnitude in Aquarius* 
Andro'meda, a northern constellation. 
A'ngle, is the inclination of two lines meeting in u 

point. 
Ano'maly, is the distance of a celestial body from Us 

aphelion. 
Antarctic Circle, is the circle which bounds the sm&h 

frigid zone. 
Anta'res, a star of the first magnitude in Scorpio- 
Antecede'ntia, the motion of a planet, contrary to the 

order of the signs. 
Antipodes, are people who live diametrically opposite 

to another. 
Anto?/ci, are people who live in the same latitude, only 

of a different name, and under the same meridian a* 

another. 
Aphelion. A celestial body is in its aphelion when si 

the greatest distance from the body it revolves &- 

round. This is called the higher Apsis. 
A'pogee, is the point in the moon's orbit farthest from 

the earth. 
Apparent conjunction of two celestial bodies, is when 

they appear to us in the same degree of I lie zodiac. 

Apparent diam'eter of a celestial, body is the angle it 
forms to the eye of a spectator on the earth* 
A ppa'rent hori'zon, is the circle which bounds our sight. 
A N psis, a point in the orbit of a celestial body at its 

greatest or least distance from the body it is revolv- 
ing round, 
A'pis, a constellation of the southern hemisphere. 
Aqua'rius, one of the zodiacal constellations. 
Aqui'la, a northern constellation. 
A'ra, a southern constellation. 
Arc, a portion of the circumference of a circle. 
Arc'tic Cir'cle, the circle which bound* the north frigM 

zone. 



ASTRONOMICAL TERMS, &C. 171 

A'returns, a star of the first magnitude in Bootes* 

Ar'go na'vis, a southern constellation* 

A'ries, the first zodiacal constellation. 

Arie'tis, a star of the second magnitude in Aries. 

Austra'lis, a southern constellation. 

Ascensional difference, is the difference between the 

right and oblique ascension or descension. 
A'scii. the inhabitants of the torrid zone, 
As'pect,the situation of one heavenly body with respect 

to another. 
Astero'ids, small planets between Mars and Jupiter. 
Astrology, a pretended art of foretelling future events by 

the aspects of the planet*. 
Astro'noray, a science which teaches the magnitudes,&c. 

&c. of the heavenly bodies. 
Alta'ir, a star of the first magnitude in Aquila. 
Atmosphere, an invisible, elastic fluid, surrounding the 

earth. &c. 
Attraction, the power with which one body or parti- 
cle of matter, leads towards another. 
Auri'ga, a northern constellation. 
AuroVa Borea'lis, meteors observed in the north. 
Austra'lis, or Piscis Notius, a southern constellation. 
A'xis, a line on which a body revolves. 
A'zimuth the bearing/Of any heavenly body from the 

meridian. 

Be'ilatrix, a star of the second magnitude in Orion. 
Bete'Igeiix, a star of the first magnitude in Orion. 
Bissextile, leap year, every fourth year. 
Bootes, a northern constellation. 

Ca'ncer, a zodiacal constellation. 

Canis Major, a southern constellation. 

Cauis Minor, a northern constellation. 

Canis Venatici, a northern constellation. 

Oanopus, a star of the first magnitude in Argo Navis. 

Cape'lla, a star of the first magnitude in Auriga. 

Cardinal points. East, west, north, and south points ©f 

the horizon. 
Cassio'peia, a northern constellation. 
Ca'stor. a star of the first magnitude in Gemini. 



TiZ A VOCABULARY OE 

Cele'stial globe, a globe representing the positions, 
magnitudes, &c. of the stars. 

Centa'urus, a southern constellation. 

Centrifugal force, is that force by which a body revolv- 
ing around another endeavours to quit its curve. 

Centripetal force, is the force by which a body revolv- 
ing around another, is drawn towards it. 

Ce'res, an Asteroid, discovered by 3YL. Piazzi, 

Cetus, a southern constellation. 

Circle, a round figure : circles are divided into great and 
small. 

Circle (Great), is a circle which divides a globe into two 
equal parts. 

Circle (Small), is a circle which divides a globe into two 
unequal parts. 

Colu'mba, a small southern constellation. 

Col'ures, two circles passing through the poles and cut- 
ting the equator at right angles : one passes through 
1° of Aries, and 1° of Libra, and is called the Equi- 
noctial Colure ; the other through 1° of Cancer and 
1° of Capricorn, and is called the Solstitial Colure. 

Co'ma Berenices, a northern constellation. 

Comet, a body in the solar system, with a shining tail. 

Conjunction of two celestial bodies, is their appearing 
in the same sign, &e. of the zodiac. 

Conseque'ntia, the real motion of a heavenly body in 
thp Zodiac, called also direct. 

Constellation, a number of stars which are imagined to 
form any particular animal, &c. 

Cor Caro'li, a star of the second magnitude. 

Cor fiy'drse, a star of the second magnitude in Hydra. 

Cor Leo'nis, a star of the first magnitude in Leo,callcd 
also Kegulus. 

Coro'na borea'lis, a beautiful northern constellation. 

Coro'na meridiana'lis,a southern constellation. 

Co'rvus, a southern constellation. 

Cosmical rising and setting, is when a star rises or sets 
at sun- rise. 

Crater, a southern constellation. 

Culmination, the passage of a star over the meridian. 

Cy'gnus, a northern constellation. 



ASTRONOMICAL TERMS, &C. ITS 

Day (artificial), the time from sun-rising to sun-setting* 

Bay (astronomical or natural), is the time elapsing be- 
tween the sun's appearing twice on the same merid- 
ian. 

Bay (siuVreal), the time elapsing between a etar's ap- 
pearing twice on the same meridian. 

Declina'tion, the distance of a celestial body from the 
Equinoctial. 

Begre'e, the three hundred and sixtieth part of the cir- 
cumference of every circle. 

Belpbi'nus. a northern constellation. 

Be'neb. a star of the second magnitude in Leo. 

Bepre'ssjon, the distance of a body below the horizon. 

Beiee'nding node, is the point where the orbit of a plan- 
et is imagined to cut the plane of the ecliptic, in going 
from a northern to a southern latitude. 

Bi'gie, the twelfth part of the diameter of the sun or 
moon. 

Bise, the face of the sun or moon. 

Bra'co, a northern constellation. 

Bel/he, a star of the second magnitude in Ursa Major. 

Earth, the planet on which we reside. 

Esst* one of the cardinal points of the horizon. 

Eccentricity, the distance of the sun from the centre of 

the elliptical orbit of a planet. 
Eeli'pse, an obscuration of light from one body by the 

interposition of another. 
EchVtic, the orbit the earth revolves in in going round 

the sun. 
Eleva'tion, the altitude of any object. 
Elongation, an angle formed by two imaginary lines ; 

©Redrawn from the earth through the sun. and the 

other from the earth through the planet, continued 

to, and measured on the ecliptic 
Equa'tion of time, is the difference between solar time, 

and mean or clock time. 
E'quinoxes, the beginning of Aries and Libra. 
Equa'tor, a circle on the earth, equi-distant from each 

pole. 
Equ'uleus, a northern constellation. 
Equinoctial, a circle in the heavens, corresponding to 

the equator on the earth. 
Eri'danus, a southern constellation. 



174 A VOCABULARY Ot 

Fa 'cute, bright spots on the sun's disc 

Fo^cus, a point in the transverse diameter of an ellipse. 

Fixed stars, stars whose position with regard to each 

other is fixed. 
Fo'malhaut, a star of the first magnitude in Australis. 

Gala'xy, the milky way. 

Ge'mini, a zodiacal constellation. 

Geoce'ntric place, the place of a celestial body as seen 

from the earth. 
Gi'bbous, the shape of the enlightened part of the moon, 

from first quarter to the full. 

Halo, a circle round the moon. 

Heavens, the expanse in which the stars, sun, planets, 

&c. are placed. 
Heli'acal, a body rises or sets heliacally when it rises or 

sets with the sun. 
Helioce'ntric place, the place of a celestial body as seen 

from the sun. 
He'misphere, the half of a sphere. 
Her'cules, a southern constellation. 
Her'schel, the fast planet in the solar system. 
Hetero'scii, inhabitants of the temperate zones. 
Hori'zon, a great circle of the sphere, dividing the 

earth into two equal parts: its poles are the zenith 

and nadir. 
Horizontal, parallel to the horizon. 
Horizontal parallax, the parallax of a celestial body 

when rising. 
Hour, the twenty-fourth part of a natural day. 
Hy'ades, a cluster of stars in Taurus. 
Hydra, a southern constellation. 
Hydra (Cor), a star of the first magnitude in Hydra. 
Hydrus, a small southern constellation. 

In'dus, a southern constellation. 

In'gress, the sun's entering any particular sign. 

Ju'no, the name of an asteroid. 
Ju'piter, the largest of all the planets. 

Kochab, a star of the second magnitude in Ursa Minor. 

Latitude, the nearest distance of any place on the earth 
to the equator. 



ASTRONOMICAL TERMS, &C. 175 

Latitude of a planet or star,is its nearest distance to the 

plane of the ecliptic. 
Lace'rta, a southern constellation. 
Leap year, every fourth year. 
Le'o, a zodiacal constellation. 
Le'o Mi'nor,a southern constellation. 
Le'pus, a southern constellation. 
Li'bra, a zodiacal constellation. 
Libra'tion, an irregularity of motion, whereby one side 

of a heavenly body is sometimes more towards the 

earth than the other. 
Line of the Aphides, a line joining the aphelion and 

perihelion of a planet. 
Lines of longitude, meridian*. 
Lo'ngitude of a celestial body, is its nearest distance to 

the plane of the ecliptic, from the first degree of 

Aries. 
Lo'ngitude of a place, is the distance of the point on the 

ecliptic, from the meridian of London, to that point 

which is nearest to the given place. 
Lu'pus, a southern constellation. 
Lynx a northern constellation. 
Lyra, a northern constellation. 

Maculae, dark spots on the sun's disc. 

Magnitudes, the apparent sizes of the stars. 

Marcab, a star of the second magnitude in Pegasus. 

Marsic, a star of the second magnitude in Hercules. 

Mars., the nearest superior planet. 

Menkar, a star of the second magnitude inCetus.. 

Machi'na pneuma'tica, a southern constellation. 

Mercury, the first and smallest of the planets. 

Meridian, a circle passing through any particular place 
and the two poles. 

Microsco'pium, a southern constellation. 

Mid-Heaven, is the point of the ecliptic upon any par- 
ticular meridian at a given time. 

Mi'lky-way, an innumerable number of stars reaching 
across the heavens. 

Minute, the 60th part of an hour, or degree. 

Mirach, a star of the second magnitude in Andromeda. 

Mono'ceros, a northern constellation. 



176 A VOCABULARY OE 

Mons me'nsae, a southern constellation. 

Month, the twelfth part of* a year. 

Mons Mce'nalus a northern constellation. £ 

Moon, the satellite of the earth. 

Mu'sca, a northern constellation. 

Musca austra'lis, a southern constellation. 

Nadir, the opposite of zenith; one of the poles of the 

horizon. 
Nebulae, telescopic stars, appearing cloudy. 
Noctu'rnal arc, the arc described by a celestial body 

from its setting to its rising. 
Nonage'simal degree, the highest point of the ecliptic 

above the horizon, equal to the angle the ecliptic 

makes with the horizon. 
Nodes, the points where a planet's orbit is imagined to 

cut the ecliptic. 
Noon (apparent), the time the sun is on the meridian ; 

12 o'clock. 
Noon (true), the time shown by a well regulated clock. 
North, a cardinal point of the horizon. 
Norma, (or Quadra Euclidis), a southern constellation. 
Nuta'tion of the axis of the earth, a iibratory motion, 

by which the obliquity of the ecliptic is affected. 

Obli'que asce'nsion, the point of the equinoctial which 

rises with the sun, or star, &c. 
Occulta'tion, the obscuration of a celestial body by the 

moon. 
Obli'quity of the ecliptic, the angle the plane of the 

earth's orbit makes with the equator ; this in 1821 

was 23* 27' 57". 
Opposition, the aspect of two celestial bodies when 

they are six signs distant. 
O'Ibers, (See Pallas.) 
Orbit, the curve one body describes in revolving around 

another. 
O'rion, a brilliant and conspicuous constellation during 

our winter months. 
Officr'na sculptoria, a southern constellation. 

Pa'llas, the name of an Asteroid. 
Parallax, the angle the semi-diameter of the earth forms 
with a celestiai body. 



ASTRONOMICAL TERMS, &C. 17? 

Parallels of latitude, small circles on the celestial globe 
parallel to the ecliptic. 

Pa'rallels of declination*, small circles on the celestial 
globe parallel to the equinoctial. 

Parallel sphere, is the position of a sphere, in which 
the equator is parallel to the horizon. 

Pa'vo, a southern constellation. 

Pe'gasus, a northern constellation. 

Penu'mbra, a faint shade surrounding the perfect shad- 
ow in an eclipse. 

Pe'rigee, the point in the moon's orbit nearest to the 
earth . 

Perihelion, the point in a planet's orbit nearest to the 
sun* 

Peri'scii, the inhabitants of the frigid zones. 

Perioe'ci, those who live in the same latitude,but on the 
opposite meridian. 

Pe'rseus, a northern constellation. 

Pha'ses, the different appearances of the enlightened 
part of the moon, or inferior planets. 

Phce'nix, a southern constellation. 

Pi v sces, a zodiacal constellation. 

Piscis Notus, a southern constellation. 

Pla'net a celestial body which revolves around the sun. 

Pleiades, the seven stars, a prominent cluster of stars 
in Taurus. 

Pointers, two stars in Ursa Major, which always point 
to the pole-star. 

Poles, the extremities of the axis of a body. 

Pole Star, a star of the second magnitude in Ursa Mi- 
nor. 

Pollux, a star of the second magnitude in Gemini. 

Praxiteles, a southern constellation. 

Prece/ssion of the Equinoxes, a slow motion of the 
Equinoxes antecedentia around the ecliptic. 

Primary Planets, bodies which revolve around the sun 
as a centre. 

Pro'cyon. a star of the first magnitude in Canis Minor. 

€tua'drant, the quarter of a circle ; a mathematical in- 
strument. 

Quadrature, the position of the moon, when three signs 

from the sun. ' _____ 

* These are seldom, or never seen on a celestial 

globe. American Editor, 



278 A VOCABULARY OE * 

duartile aspect; marked n , the position of two celes- 
tial bodies when three signs distant. 

Has Alge'thi, a star of the third magnitude in Hercules. 
Has Aiha v gus, a star of the second magnitude in Serpen- 

tarius. 
Rasta'ben, a star of the second magnitude in Draco. 
Ka'dius, the half of the diameter of a circle. 
Refra'ction bending of the rays of -light, in passing 

from a rarer to a denser medium. 
Re'gulus, a star of the first magnitude in Leo. 
Retrograde, the same asantecedentia. 
Revolution, the period of a celestial body.! 
Ri'gel, a star of the first magnitude in Orion. 
Right asce'nsion, the point of the equinoctial which 

comes to the meridian with any celestial body. 

Sagi'tta, a northern constellation. 

Sagitta'rius. a zodiacal constellation. 

Sa'ros, Chaldean Saros, the space of 18 years, 11 days, 

7 hours, 43 minutes, 20 seconds ; the time in which 

eclipses exactly return. 
Satellites, secondary planets or moons, revolving 

around the primary planets, 
Saturn, a superior planet, having seven satellites. 
Scheat, a star of the second magnitude in Pegasus. 
Schedar, a star of the third magnitude in Cassiopeia. 
Scorpio, a zodiacal constellation. 
Scutum Sobieski, a northern constellation. 
Second, the 60th part of a minute. 
Serpens, a northern constellation. 
Serpenta'rius, a northern constellation. 
Se'xtant, a mathematical instrument ; the sixth part of 

a circle. 
Sextans, a southern constellation. 
Sextile aspect, the position of two celestial bodies when 

they are two signs distant. 
Side'real day,ihe time which elapses between a star's ap- 
pearing twice on the same meridian ; it is 23 hrs. 56 x 

4".l. 
Sidereal Year, the time which elapses between the sun's 

appearing twice in conjunction with the same star. 
Sign, the twelfth part of the ecliptic ; 50°. 
Si'rius, (be brightest star in the heavens, situated in Ca- 

ftis Major. 



ASTR0N0NIC1L TERMS, &C. 179 

Situ'la, a star of the third magnitude in Aquarius. 

Solstices, the time the sun enters Cancer and Capricorn. 

South, a cardinal point in the horizon. 

Sphere, a globe. 

Spi'ca, a star of the first magn itudein Yirgo. 

Stationary, the position of a heavenly body,when it ap- 
pears to remain at one place for some time. 

Sun, the grand luminary of day. 

Sy'zygies, the conjunction and opposition of a planet 
with the sun. 

Tangent, a line touching a circle, perpendicular to 
the radius which connects it with the centre. 

Taurus, a zodiacal constellation. 

Terminator, an imaginary line which divides the light 
hemisphere from the dark. 

Tides, the rising and falling of the waters of the ocean. 

Time, the measure of duration, depending on the revo- 
lution of the celestial bodies. 

To'ucan, a southern constellation. 

Transit, the passing of an inferior planet over the sun's 
disc. 

Tropics, two circles bounding the torrid zone. 

Twilight, the faint light before sun-rising and after sun- 
setting. 

Taurus Poniato'wski, a northern constellation* 

Triangulum, a northern constellation, near Arietis. 

Tri'angulum Mi'nus, a northern constellation. 

Triangulum Austra'le, a southern constellation. 

Telesco'pium, a southern constellation. 

"Wria, a star of the third magnitude in Aquila. 

Ve'ga, a star of the first magnitude in Lyra. 

Ye'nus, the brightest of the planets. 

Vertical circles, imaginary circles, passing through the 
Zenith and Nadir. 

Ve'sta. one of the asteroids. 

Vi'a, La'ctea, the milky way. 

Vindemi'atrix, a star of the third magnitude in Virgo. 

"Vi'rgo, a zodiacal constellation. 

'Umbra, the conical shadow of the earth or moon in an 
eclipse. 

Yulp'ecula et A'nser, a northern constellation. 



180 A VOCABULARY, &C» 

XTra'nus, a name sometimes given to the planet Her* 

schel. 
Ursa Major, a very conspicuous northern constellation, 
Ursa Minor, a northern constellation, in which the pole 

star is situated. 

X'iphias, a southern constellation. 

Year (a solar), the space of 365 days, 5 hours, kW 48". 

Year (a sidereal), the space of 365 days, 6 hours, 9' 12", 

Zenith, the point exactly overhead ; one of the poles of 
the horizon. 

Zodiac, the space in which all the planets move in re« 
volving around the sun. 

Zone, a division of the earth : there are five zones. 

Zubenelg, a star of the second magnitude in Libra. 

Zubenesch, a star of the second magnitude in Libra. 

Zub'enna, lira'bi, a star of the second magnitude in Li- 
bra. 



THE EN J*, 



QUESTIONS 

OH 

TREEBY'S ELEMENTS 

OS 

DESIGNED 

MORE EFFECTUALLY TO FACILITATE THE PROGRESS 
OP THOSE WHO USE THAT VALUABLE WORE, 



By S. TREEBY, 



PREFACE. 



It is quite superfluous to attempt to state the 
advantages attending the interrogatory system 
of education: its universal adoption is an unan- 
swerable argument of its utility : hut while 
geography, history, and the belles lettres, are 
cultivated in seminaries by the fertilizing hands 
of interrogatories, the most noble of all sciences 
has hitherto been left wildly to shoot, without 
the assistance of any guide excepting nature* 
The present book of questions is founded on a 
work which has long been found wanting in 
English schools ; and is, for conveniency's sake, 
divided into four parts ; the first comprises about 
Five Hundred Questions.outhe numbered articles 
in Part 1. The Elements of Astronomy : and, as 
they bear immediately on the facts interspersed 
therein, they require no other assistants to de- 
velope their answers, than an attentive perusal of 
that portion of the work. They are intentionally 



184 PREFACE, 

irregularly arranged, which arrangement is a man- 
ifest advantage, inasmuch as it tends to quicken 
the memory, and to mature the understanding 
of the learner. The second part contains near- 
ly Eighty Questions on the observations which 
succeed the numbered articles as illustrations, 
deductions, inferences, proofs, &c. in that part 
of the work : among which may be found clearly 
illustrated, the methods astronomers have had 
recourse to for ascertaining the magnitudes, 
periods, distances, &c. of the planetary bodies, 
by which they have determined the times they 
revolve on their axis, their elliptical orbits, the 
nature and causes of their accelerated and ret- 
rograde motions, and their stationary appear- 
ances ; how the longitudes of places on the earth 
may be found by means of the eclipses of the 
moon, the satellites of Jupiter, or by the culmi- 
nation of the fixed stars ; proofs of the rotundity 
of the earth ; an easy method of calculating the 
return of eclipses, &c. ; which observations re- 
quiring more judgment to be understood, than 
the facts which are numbered, questions on them 
will consequently serve as criterions for deter- 
mining whether the pupil's understanding keeps 
pace with his memory, and may therefore be used 



PREFACE. 185 

according to the discretion of the intelligent 
teacher. 

The third pari includes nearly Sixty Ques- 
tions on 4 The Planetary Problems ' in Part II. 
of The Elements ; these, as well as the others are 
irregularly arranged, and will therefore, more 
completely answer their design. The fourth and 
last part comprises questions on 'The Problems 
on the Globes ;' amongst them are several on 
the Geographical and Astronomical Definition^ 
&c. in Part III. of ' The Elements / these will 
be fouud to be inferior to none extant for the pur- 
poses of examining the pupil in that department 
of ornamental, instructive, pleasing, and useful 
literature. 

Plymouth, December \2ih % 1821. 



PART I. 
QUESTIONS 

BEARING DIRECTLY ON THE FACTS 

IN THE 

ELEMENTS OF ASTRONOMY. 

To be answered by the Student in writing. 



1. Which of the planets have satellites? 

2. What is the longitude of a planet ? 
S. What are secondary planets ? 

4. What is astronomy ? 

5. What is the office of a secondary planet ? 

6. Upon what is physical astronomy founded ? 

7. How many planets are there in the solar system ? 

8. What is meant by the length of a planet's day ? 

9. How long does Mercury take to revolve on its 
axis ? 

10. Have the inhabitants of Venus any morning and 
evening star ? 

11. How are the solar spots divided? 

12. What is meant by the orbit of any celestial body ? 
IS. How many kinds of motions have the planets? 

14. How do you determine the earth's, and the son's 
places in the ecliptic ? 

15. Which are the solstitial days ? 

16. What is meant by the sun's declination ? 

17. Does Mercury ever transit the sun ? 

18. How many signs are In the ecliptic, and name 
them? 



188 QUESTIONS TTPON THE 

19. What proportion is there between the speeiriu 
gravities of water and air ? 

20. In what sign does the planet Venus intersect the 
plane of the ecliptic? 

21. What body is in the centre of the solar system ? 
29. What is meant by the direct motion of a planet? 

23. What is meant by the diurnal and nocturnal arcs 
of the sun, a planet, or star ? 

24. In what part of its orbit was the comet of 1819, 
when visible to us ? 

25. How is snow occasioned ? 

26. What is Venus poetically called when she is an 
evening star ? 

27. What is meant by a planet's orbicular motion ? 

28. In what direction is the motion of the earth ? 

29. How long is the solar day ? 
SO. How long is a solar year ? 

31 . How long does the earth take to revolve from any 
particular portion of the ecliptic, until it arrives there 
again ? 

3% What are primary planets ? 

33. How far does the zodiac extend on each side of 
the ecliptic ? 

34. When is the sun's declination the greatest ? 

35. \V hat are the tropics ? 

36. What are clouds ? 
3T. What is a lunation ? 

38. What is a parallax ? 

39. What is the diameter of Jupiter? 

40. What effects have heat and cold upon our atmos- 
phere ? 

41. When is the earth in the equinoxes ? 

42. How long is a solar year ; and which is the lon- 
ger part, the summer or the winter ? 

43. Where is Jupiter's ascending node? 

44 What did the ancients consider the sun to be ? 

45. What is the difference between a planet and a 
comet ? 

46. What is the axis of a celestial body ? 

47. Is the earth nearer to the sun in the winter or in 
the summer ? 

48. What is hail? 

49. Who discovered the planet Herschel ? 



ELEMENTS OB ASTRONOMY. 189 

50. In what part of the ecliptic is the ascending node 
of Saturn ? 

51. Why was the name of Mercury given to that 
planet which is nearest to the sun? 

52. What is a planet? 

5S. How long is Saturn revolving round the sun ? 

54. What is a comet, and how long was the tail of 
the comet of 1819 ? 

55. What are falling stars ? 

56. At what time of the day is it likely to see the 
planet Mercury ? 

57. How long is Mars revolving around the sun ? 

58. How are planets divided ? 

59. How are the different seasons occasioned ? 

60. What is lightning ? 

61. By what character is Saturn expressed ? 

62. Wkatisamistor fog? 

65. What kind of curve do the planets describe in re- 
volving around the sun ? 

64 What effects are produced by the inclination of 
the axis of the earth ? 

65. What is a central eclipse ? 

66 Which is the longest day in the year in a southern 
latitude ? 

67. What are the two extreme points of the axis of a 
body called ? 

68. What appearance has Saturn to the naked eye? 

69. How long does Jupiter take to revolve on its axis? 

70. On what days is the declination of the sun noth- 
ing? 

71. Define the equator. 

72. How long does the earth require to revolve on its 
axis? 

73. What is the name of that circle called which 
bounds the North Frigid Zone ? 

74. What are the effects of the rotation of the earth 
on its axis ? 

75. How far over the North Pole do the sun's rays 
extend on the longest day, or June 21st? 

76. What star is it that always appears in one posi- 
tion ? 

77. What ig meant by the conjunction ef two celes- 
tial bodies ? 



190 QUESTIONS UPON THE 

73. Are the solar days always of the same length I 3 

79. When has the sun no declination ? 

80. What is thunder? 

81. How far distant is Herschel ? 

82. What is the name of the line 'about which the 
earth Querns to revolve ? 

83. What is meant by a planet's daily motion ? 

84. How many satellites are there in the solar system? 

85, How is Astronomy divided ? 

86. What is meant by the heliocentric longitude of a 
planet ? 

87 Into how many degrees is the circumference of 
the earth divided ? 

88. Are the dews heavier in hot or in cold countries ? 

89 How far distant i* Mars from the sun ? 

90. What is an occupation? 

91 Repeat Pope's description of the moon. 

92- What is the ecliptic ? 

95. What do modern astronomers consider the sun to 
be? 

94. What is a partial eclipse ? 

$5* ~nto how many kinds are conjunctions divided ? 

96 Which planets have an inferior and superior con- 
junction ? 

97. What is meant by the stationary appearance of a 
planet ? 

98. When Venus is a morning star is she to the east, 
or to the west of the sun ? 

99. What is the reason that the fifth planet in the so- 
lar system is named Jupiter? 

100. What is the diameter of Mars ? 

101. How are the celestial bodies divided ? 

10*2. What is meant by the precession of the equinox- 
es ? 

103. What is physical astronomy ? 
104- Name the zodiacal constellations. 

105. What is the greatest elongation of Mercury ? 

106. By what is the earth attended in its motion round 
the sun ? 

107. Of what does the solar system consist ? 

108. Who first discovered the phases of Venus ? 

109 What is the quantity and direction of the pre* 
cession of the equinoxes ? 



ELEMENTS OE ASTRONOMY. 191 

110. How long does the earth take to revolve around 
the sun ? 

111. What clouds generally produce rain ? 

112. How is it, that the moon at her opposition ap- 
pears entirely enlightened ? 

113. What is understood by the meridian of any par- 
ticular place ? 

114. What effects are produced, when the clouds 
which produce lightning, are very low ? 

115. How far are the asteroids distant from the sun ? 

116. What is the eciiptic ? 

117. What is the elongation of a planet ? 

118. W r hat is the probable cause of the changes of 
the weather, at the new and full moon ? 

119. What is the twilight ? 

120. How is Venus poetically described by Baker ? 

121. What is the horizon of any particular place i 

122. Of what does the universe consist ? 

123. W r hatis meant by the opposition of the celestial 
bodies ? 

124. How many comets have already been observed ? 

125. At what part of the day does the sun appear oa 
the meridian of any particular place ? 

126. What are the polar circles ? 

127. What is a temperate zone ? 

128. W r hen is a planet said to move in a retrograde 
direction ? 

129. Does Venus ever transit the sun ? 
ISO. How is dew generated ? 

131. How many stars are discernible in a clear even- 
ing ? Lets ? 
132- Which in appearance is the darkest of the plan- 

133. How long are the asteroids revolving round the 

134. What is pure astronomy ? [sun ? 

135. How long is the planet Herschel revolving round 
the sun ? 

136. What is the shape of the earth ? 

137. When Mercury transits the sun, what appear- 
ance has it on the sua's disc ? 

138. On what days is the earth in the equinoctial 
points ? 

139. What is the grand reservoir of dews ? 

140. What are the belts, of Jupiter considered to be ? 



192 auESTIONS UPON THB 

141. How are the planets divided ? 

142. How long was the tail of the comet of 1680 t 

143. How long does Venus take to revolve around 
the sun ? 

144. With what is the surface of the moon interspers* 
ed ? 

145. Which is the least planet in the solar system ? 

146. Where is Jupiter's descending node ? 

147. x\re the asteroids visible to the naked eye ? 

148. What is the diameter of Herschel ? 

149. How is pure astronomy determined ? 

150. What is the source of rain and dews ? 

151. When will the next transit of Venus be ? 

152. Has Jupiter any spots on his surface ? 

153. Do the stars shine by reason of the sun's light ? 
154- Which planets have both an inferior and superi- 
or conjunction ? 

155. When does the retrograde motion of an inferior 
planet happen ? [cer ? 

156. On which side of the equator is the tropic of can- 

157. What is meant by the obliquity of the ecliptic ? 

158. How far distant is Mercury from the sun ? 

159. What is the zodiac ? 

160. By what character is Jupiter distinguished ? 

161. What is meant by the harvest moon ? 

162. What is solar time ? 

163. Would a bowl upon a hill, or upon the surface of 
the eartn receive the greater quantity of water during 
the same shower ? 

164. When was the planet Herschel discovered ? 

165. How many satellites has Saturn ? 

166. Does the dew descend the more copiously upon 
the earth after a hot or a cold day : and why ? 

167. What parts of the ecliptic are called solstitial 
points ? 

168. By what character is Mercury distinguished ? 

169. Into what are the bodies which revolve around 
the sun divided ? 

170. What is meant by a planet's heliocentric place ? 

171. Why is the particular situations of the sun. plan- 
ets, comets, &c. with respect to each other, called the 
solar system ? 



ELEMENTS OE ASTROWOMY. 195 

1?2. To what are the diversified colours of the clouds 
Owing > 

173. In what city was it that the celebrated astronomer 
Herschell discovered the planet which bears his name ? 

174. How long is Saturn revolving on its axis ? 

175. In what position is the axis of the earth with re- 
spect to the plane of the ecliptic ? 

176. What appearances have the mountains, islands, 
&c. of the earth, to the inhabitants of the moon ? 

177. What is the size of thetearth ? 

17&- How does Thomson beautifully describe the sun? 

179. How many asteroids are there in the solar system? 

180. What is meant by the horizontal parallax of a 
celestial body ? 

181. What does an annular eclipse mean ? 

182. What are tides? 

183. By what characters are the planets distinguished? 

184. To what are the various shapes of clouds owing ? 

185. How are the inhabitants of Jupiter compensated 
for their defect of the light of the sun ? 

186. How many temperate zones are there ? 

187. By what is the earth surrounded ? 

188. What angle does the orbit of Mars make with 
the plane of the ecliptic ? 

189. How do astronomers prove the ring of Saturn to 
be a solid body surrounding that planet ? 

190. How many kinds of motion is the earth endued 
with ? 

191. What effects are produced by the rotation of a 
secondary planet on its axis ? 

192. Between which two planets is "Venus situated ? 

193. How have astronomers determined the height of 
the mountains of the moon ? 

194. Which is the third planet in the solar system ? 

195. Where does the orbit of Mercury appear to cut 
the plane of the ecliptic? 

196. How is it that the sun, which is stationary, ap- 
pears to rise, attain its meridian splendour, and to set ? 

197. What is the difference between a solar and a si- 
dereal day ? 

198- What is the greatest elongation of V«nui ? 

17 



194 (AlJESTIOtfS TO>N THE 

199. W hat is the office of the moon ? 

200. What are clouds ? 

201. What kind of curve do comets describe in revol- 
ving round the sun ? 

£02- Are the clauds all of one height ? 

£03. What is the length of time the earth is revolving 
around the sun called? 

204. Which planet mostly resembles the earth ? 

£05. How long is the moon in revolving from one fix- 
ed star, before it returns to it again ? 

206. What is the circle called which bounds the south 
Frigid Zone ? 

207. How do you prove that the revolution of the 
earth on its axis, is from west to east ? 

£08. How do you determine the space the earth pro- 
ceeds in its orbit, during one revolution on its axis ? 

209. What proportion of light and heat does Jupiter 
receive, compared to that which invigorates the earth ? 

£10. What character is used to distinguish the planet 
Herschell ? 

£11. How is the apparent motion of the stars occasion- 

£1£. What is a total eclipse ? [cd ? 

213. How large is the planet Herschell to^the naked 
eye ? [moon ? 

£14. Why must eclipses of the sun happen at new 

£15. What does the middle section of the earth con- 
tain ? 

£16. Is the motion of the earth in the ecliptic uni- 
formly equal, in two equal measures of mean time? 

£17. Of what use is the atmosphere to us ? 

£18. What are the names of those points where the 
orbit of Mercury is imagined to intersect the ecliptic ? 

219. What are inferior planets ; and why are any so 
so called ? 

£20. Which is the nearest of the superior planets ? 

£21. What is meant by a planet's retrograde motion ? 

222. In what parts of the ecliptic are the equinoctial 
points placed ? 

££3. How often do the tides rise ? 

££4. What composed the body of the telescope, with 
wbicu Galileo discovered the satellites of Jupiter ? 

22& How large is the sun>and how large is the moon ? 



ELEMENTS 0E ASTRONOMY. 195 

226. What proportion has the sun to the moon in 
raising the tides ? 

227. What is remarkable of the atmosphere of the sun? 
223. Are the drops of rain larger or smaller at the 

surface of the earth, or when they first descend from the 
clouds ? 

229. How long would the'night be to the inhabitants 
of/Jupiter, if his axis were much inclined ? 

230. With what force does the atmosphere press upon 
the earth ? 

231. How long was the tail of the comet of 1811 ? 

232. What reason can be assigned for the stars ap- 
pearing so very numerous ? 

233. What is the aurora borealis ? 

234. What is the reason that the summer half year is 
longer than the winter ? 

235. Which are the superior planets ; and why are 
they so called ? 

236. What is remarkable of the belts of Jupiter ? 

237. Does the sun move round the earth as was for- 
merly supposed, or does the earth move round the sun ? 

238. When Venus is a morning star, what is she po- 
etically called ? 

239. How would the sun appear if there were no at» 
mosphere surrounding the earth ? 

240. Which are the principal constellations ? 

241. What is meant by the geocentric longitude of a 
planet ? 

242. Which of the planets shines so brilliantly as to 
cause objects which it illuminates to cast a shadow ? 

243. Which is the only body in the solar system that 
shines by its own light ? 

244. How do you know that the earth is nearer to the 
sun in the winter, than it is in the summer ? 

245. Which is the most brilliant of the planets ? 

246. What is the greatest height to which clouds as- 

247. Why is the natural day called a solar day ?§cend? 

248. How is the atmosphere essential in rarefying the 
noxious effluvia which arise from the earth ? 

249. Which was anciently considered the most distant 
planet in the solar system ? 



1% QUESTIONS UPON THIS 

250. How many stars did the astronomer HerschelJ 
count in a small portion of the milky way ? 

251. What is meant by a sextile aspect ? 

252. Where is the planet Saturn's descending node ? 

253. AVhat does an inferior conjunction mean ? 

254. AVhat advantages are derived to astronomy by 
the satellites of Jupiter ? 

%55. What is a synodical month ? 

256. How long is the sun revolving on its axis? 

257. Is Mercury a primary or a secondary planet ? 
%5$. What is the distance of the earth from the sun ? 

259. How may I know when any planet is in opposi- 
tion to the sun ? 

260. What is meant by a planet's apparent place ? 

261. How far is Yenus distant from the sun ? 

262. (The equator excepted,) the day and night is 
unequally divided throughout the year, excepting two 
days ; which are they ? 

263. How is the progressive motion of light proved ? 

264. How is the length of the sidereal day determined ? 

265. On which side of the equator is the tropic of 
Capricorn ? 

266. W r hat is the greatest portion of the earth th© 
mn does not shine on in a day ? 

267. AVhat is meant by the parallax of the earth's an- 
nual orl»it? 

268. Why do eclipses happen irregularly ? 

269. When a planet is in opposition to the sun, how 
far is its place from the earth's place, and how far from 
the sun's ? 

270. Which are the more frequent, eclipses of the sun, 
or of the moon? 

271. How is the immovable appearance of the polar 
star occasioned ? 

272. What is the reason that Venus is never visible 
during the night ? 

273. What is the most general height of the clouds ? 

274. Are the satellites of Jupiter discernible by the 
naked eye ? 

275. What is remarkable in the periodic times of tb» 
comets ? 



KL1MEKTS «E ASTRONOMY. 197 

276. How does the firmament appear when viewed 
through a telescope ? [pect ? 

277. When have any two celestial bodies a trine as- 

278. How is it that an eclipse of the moon is visible 
to every place where she is visible ? 

279. What did Sir Isaac Newton say the tails of com- 
ets were ? 

280. How far does the atmosphere of the earth extend 
from its surface ? 

281. Is the atmosphere denser or rarer in the upper 
regions ? 

282. How is the solid body of the earth divide*! ? 

283. What is a sidereal day? 

284. Of what nature are the stars supposed to be ? 

285. What is the milky way ? 

286. What is meant by one planet's having a quartile 
aspect with regard to another ? 

28T. What is a superior conjunction ? 

288. In what direction is the axis of Jupiter compared 
with the plane of the ecliptic ? 

289. Who had the honour of discovering the satellites 
of Saturn ? 

290. What is the ring of Saturn ? 

291. Into how many zones is the earth divided ? 

292. How long does Venus take to revolve on her axis? 

293. What is the exact period that Mercury takes to 
revolve around the sun ? 

294. How many signs is the geocentric from the helio- 
centric place of a planet, when such planet is in an infe- 
rior conjunction ? [duce? 

295. What does the external section of the earth pro- 

296. What is the greatest number of eclipses that can 
happen in a year ? 

297. How long is the sidereal day ? 

298. What is the comparative lengths of the days on 
the earth and at the moon ? 

299. How many asteroids are there, and by whom 
were they so named ? 

300. What is meant by the parallax of a celestial body? 

301. What other name is given to tke planet Herschel)* 
$nd why ? ' 

17* 



193 aUESTIONS UPOW THE 

302. How much denser is the atmosphere of the gun, 
than the atmosphere of the earth ? 

303. How far does the zodiac extend from the plane 
of the ecliptic ? 

304. When does the retrograde motion of a superior 
planet happen ? 

305. What proportion is there between the altitude of 
the Pole Star, and the latitude of any particular place ? 

306. In what direction do the moon's nodes move ? 
SOT. What is remarkable ©f the solar spots ? 

808. What is the nearest distance of any celestial body 
to the plane of the ecliptic called ? 

309. What is the least number of eclipses that can 
happen in any year ? 

3»0. What is meant by a planet's retrograde motion ? 

oil. Pow is the Zodiae divided ? 

312. In what part of her orbit is the moon, when she 
is eclipsed ? 

S13. How long is the moon revolving on her axis ? 

314. What is meant by the equation of time ? 

315. By what means do we derive light from the sun 
before he rises, and after he sets ? 

S16. How long is Mars revolving on its axis? 

317. If a body weigh a pound on the surface of the 
earth, what would it weigh if it were removed to the 
surface of the moon ? 

318. Suppose the moon's orbit jjwere situated in the 
plane of the ecliptic, how often would eclipses happen ? 

319. To what is the red appearance of Mars owing? 

320. Within what distance of the horizon is the sun, 
when twilight commences in the morning, and ends in 
the evening ? 

321. Of what is the internal section of the earth com- 
posed ? 

322. By whom were the solar spots first discovered ? 

323. Mark the characters used to distinguish the 
constellations of the Zodiac. 

324. What is a frigid zone ? 

3%5. Do the rays of the snn ever enlighten both the 
poles of the earth at the same time ? 
326. What is a total eclipse ? 



ELEMENTS OE ASTRONOMY. i9£ 

S£T. How many constellations are there north of the 
Zodiac ? 

528. How l©ng was the Astronomer Herschell coun« 
ting 116,000 stars ? 

S2% How long can a lunar eclipse continue ? 

330. How is an eclipse of the sun occasioned ? 

SSI. What are these different points of the ecliptic call- 
ed, where the orbits of the planets seem to cut its plane? 

332. Which is the first planet in the solar system ? 

333. Why is Mercury called an inferior planet ? 

334. How many frigid zones are there ? 

535. What is a day ? 

53 6. How long does Jupiter take to revolve around 
the sun ? 

337. Why are there more visible eclipses of the moon 
than of the sun, at any particular place ? 

338. Which planet, when viewed through a telescope, 
has phases like the moon ? 

339. Why is the orbit of the earth, called the ecliptic? 

340. What is meant by the declination of the sun ? 

341. How far does the torrid zone extend ? 

342. What is an hour? 

343. What is the distance of the moon from the earth? 

344. What character is used to represent Mars ? 

345. How far distant is Jupiter from the sun ? 

346. When Jupiter is in opposition to the sun, how 
far is he from the earth ? 

34T. When Jupiter is in conjunction with the sun, 
how far is he from the earth ? 

348. What angle does the axis of Mars make with a 
perpendicular to the plane of its orbit ? 

349. What advantage, besides proving the progres- 
sive motion of light, do we derive from the discovery of 
the satellites of Jupiter ? 

350. Why must the moon be in one of her nodes to 
eclipse the sun ? 

351. How long can the moon be totally eclipsed ? 

352. How is the ascending node of a planet marked ? 

353. Which planet revolves around the sun in the 
shortest space of time ? 



100 CtTJESTIONS UPON THE 

354. How long does Venus continue a morning and 
an evening star alternately ? 

355. How does the poet Baker describe Mercury ? 

356. What is a solar day ? 

357. Which is the most resplendent body in the 
heavens, next to the sun ? 

358. In what direction does the moon revolve around 
the earth ? 

359. What are the bright spots near the poles of Mars 
considered to be ? 

360. What is meant by the term digit ? 

361. What is the diameter of Mercury ? 

362. How is the descending node of a planet marked? 

363. What is the torrid zone ? 

364. How many kinds of days are there ? 
S65. What is mean time ? 

366. How long is the moon making a complete revo- 
lution around the earth ? 

367. Why is the fourth planet in the solar system 
called Mars? 

368. How many satellites has the planet Herschell ? 

369. Between which planets are the asteroids ? 

370. What particular advantages result to astronomy 
from the various aspects of the planets ? 

371. Is Mercury an inferior or superior planet? 

372. What is Venus called when she appears in the 
morni n g i and what when she is visible in the evening? 

373. What is meant by the sun's path in the heavens? 

374. On what part of the earth are the days and 
n »»hts always equal ? 

375. Is Venus a superior or an inferior planet ? 
$76. In what portion of her orbit is the earth, when 

the day is equal to the night all over its surface ? 

377. What are the boundaries of the torrid zone called? 

378. What other names are given to the solar day ? 

379. What kind of a body is the moon ? 

380. How many aspects have astronomers divided the 
configuration of the celestial bodies into ? 

381. How is the retrograde motion of an inferior 
planet occasioned ? 

382: What kind of motion do the stars appear to have ? 



ELEMENTS OE ASTRONOMY. 



SOI 



383. How are the phases of the moon occasioned ? 

384. In what direction do the moon's nodes move J 

385. Which planet is the farthest from the sun ? 

386. How many satellites has Saturn ? 

387. How many constellations are there ? 

388. Name the principal stars visible in our winter 
evenings. 

389. What curve does the moon describe in revolving 
around the earth ? 

390. Which is the fifth planet in the solar system? 

391. Where is the ascending node of Mars? 

392. Which is the brightest of the stars, and in what 
constellation is it ? 

393. In what degree are the stars magnified, when 
viewed through a telescope ? 

394. What is the moon's mean motion in a day ? 

395. What proportion is there between the densities 
of the atmospheres of the earth and moon ? 

396. Which is the largest planet in the solar system ? 
39T. How do astronomers determine the distance of 

Mars ? 

398. What letter do the principal stars in the con- 
stellation Cassiopeia represent ? 

399. Between which planets is Jupiter ? 

400. In which of the constellations are the Pleiades ? 

401. Why is Jupiter called a morning and an eve- 
ning star ? 

402. In what portion of her orbit is the moon when 
she appears semicircular? 

403. How many degrees do the moon's nodes move in 
a year ? 

404. Has the moon any atmosphere ? 

405. How do you know that Mars is farther from the 
sun than the earth is ? 

406. Who first determined the time that Mars is re- 
volving on its axis ? 

40T. What is the surface of Jupiter interspersed with? 
408* Has Saturn any spots on its surface ? 

409. Who first discovered the ring of Saturn ? 

410. In what proportion are the planets magnified 
when viewed through a telescope ? 



202 fcFBSTIOffg tTPOX THJB 

411 # How large was the comet of 1811 ? 

412. How are the tides occasioned ? 

413. What kinds of bodies were comets formerly con- 
sidered to be ? 

414. What is the greatest distance that Saturn can be 
from the plane of the ecliptic ? 

415. Which is the least splendid of the planets ? 

416. From the conjunction to the opposition of the 
moon, is the enlightened part of her circumference to- 
wards the east or west ? 

417. Of what practical utility are the occultations of 
any of the planets or stars ? 

418. How is the character for conjunction made? 

419. What is a periodical month ? 

420. How old is the raoon when she sets at sun rising? 

421. Why are the tides higher at new and full moons 
than at other times ? 

422 Which are the principal northern constellations? 

423. What is an eclipse ? 

424 Observing the raoon, I perceived she was 
semicircular, and her enlightened edge was towards the 
east ; how old was she ? 

425. What angle does the orbit of the moon make 
with the plane of the ecliptic ? 

426. When eclipses of the sun happen, of what age is 
the moon ? 

427. What is meant by a planet's real, or direct mo- 
tion or place? 

428. W hat uses were the observations of the aspects of 
the planets applied to by astrologers ? 

429. What is meant by the moon's nodes? 

430. Which is the fourth planet in the solar system ? 

431. What is the horizontal moon ? 

432. What is the period of Jupiter ? 

433* How is the retrograde motion of a superior plan- 
et occasioned ? 

434. How do the planets move round the sun ? 

435. What is meant by the stationary appearance of a 
planet ? 

436c How is an eclipse of the moon occasioned ? 



ELEMENTS OS ASTKOtfOMT, 20S 

45?. Do eclipses of the sun appear to all places on the. 
earth, where the sun is visible at the same time ? 

438. Can astronomers determine the distances of the 
Itars? 

439. How many stars are there of the first, second, 
third, fourth, fifth, and sixth magnitudes ? 

4M> How many southern constellations are there ? 

441. For what purpose were the stars divided into 
constellations? 

442. Why cannot astronomers tell the distances of the 
stars, as well as the distances of the sun, moon, or plan- 
ets ? 

443. What effect is produced by a light shining on a 
dark body ? 

444. How many inferior planets will an inhabitant of 
Mars have ? 

445 What has been observed near the poles of Mars? 

446. How is it. that the moon, which is one of the 
least of the heavenly bodies, appears one of the largest ? 

44T. What angle does the axis of the moon make witk 
a perpendicular to the plane of the eciiptic ? 

448. Which is the brightest planet to the inhabitants 
Of Mars ? 

449. In what part of her orbit is the moon at the 
time of new moon ? 

450. Which of the planets, besides Jupiter, has belts ? 

451. How old is the moon when she appears on the 
meridian at midnight ? 

45^. What did Sir I. Newton say comets were ? 

453. Whai is the length of the longest day to the in- 
habitants oi Jupiter ? 

454. By what is Saturn circumscribed ? 

455. What is tb.; diiference between a periodical and 
% synodical month ? 

456. How many satellites has Jupiter ? 

457. What is the distance of Haturn T 

458. Who first ranked comets among the bodies of 
the solar system ? 

459. What is the diameter of Saturn ? 

460. What are the changes in the appearances of 
»oon called ? 



204 QUESTIONS UPON THfi 

461. What other bodies besides planets and asteroids, 
belong to the solar system ? 

462. What are Syzygies ? 

463. What is meant by the conjunction of the sua 
and moon ? 

464. When is the moon said to be in conjunction $ 

465. Do comets go very near to the sun ? 

466. In what part of her orbit is the moon when 
nearest to the sun ? 

467. How far distant was the comet of 1811, when 
nearest to the earth ? 

468. In what part of her orbit is the moon at full 
moon ? 

469. What did Sir I. Newton say respecting the heat 
of the comet of 1680? 

4T0. When is the moon in that part of her orbit which 
is farthest from the sun ? 

471. How long did Sir I. Newton say the comet of 
1680 would require to get cold ? 

472. How many kinds of eclipses are there ? 

473. What figure will be generated by the rays of a 
larger luminous body shining on a smaller opaque glob- 
ular one ? 

474. Whatportion of her orbit must the moon be in 
to eclipse the sun ? 

475. How is it that the moon is visible to us at the 
time of her conjunction ? 

476. Is it at new or full moon that the moon rises at 
sun -set ? 

477» What is the precession of the equinoxes? 

478. By what power are the celestial bodies preserv- 
ed in their orbits? 

479« How many days have the inhabitants of the moon 
in a year ? 

480. How many comets have already been observed ? 

481. In what direction do the equinoxes move, and 
how many seconds in a year is that motion ? 

482. Of what shape ape the orbits ofall the planetary 
bodies? 

483. What is the foundation of all motion? 

484. How many stars is the firmament imagined to 
contain ? 



"ELEMENTS Off ASTRONOMY. 205 

485. What is the first division of time ? 

486. How are the fixed stars distinguished from the 
planets? 

487. What is meant by the term year ; and how long 
is the year respectively at each of the planets ? 

488. What is the reason that the distances and peri- 
ods of comets cannot be determined, as well as the dis- 
tances, periods, &c. of the planets ? 

489. By whom was the power of gravitation first 
proved to exist ? 

490. In what direction does the moon revolve on her 
axis ? 

491. How long is a day at the moon, compared with 
a day on the earth ? 

492. What is time ? 

493. By what power are the celestial bodies preserv- 
ed in their respective orbits ? 

494. The inhabitants of which planet have the short- 
est days ? 

495. What is the difference in the appearances of the 
planets and stars, when viewed through a telescope ? 

496. What bodies are imagined to be continually re- 
volving around every fixed star ? 

497. What is the difference between an occultation and 
a transit ? 

49c. On what day does the earth enter =£k ? 

49;). Which of the celestial bodies has the greatest pa* 
rallax, and why ? 



18 



206 auESTiONs xrpoff the 

PART II. 



QUESTIONS 

BEARING ON 

THE OBSERVATIONS. 

To be answered by the Student in writing. 



500. How is the circumference of every circle divided' 

501. Prove to me by a diagram, that it is not possible 
to see an inferior planet in the night. 

502. How do astronomers determine the distance the 
earth is from the sun ? 

505. How do you explain the inequalities in the lengths 
of the solar days ? 

504. Illustrate the variation in the declination of the 
sun. 

505. How long would light be travelling from us to 
the nearest fixed star ? 

506. How do you determine the time the moon is re- 
volving on its axis ? 

507. Tell me the causes of the variations in the sea* 
sOns. 

508. What curve does each planet describe in revolv- 
ing around the sun ? 

509. How do you illustrate the apparent diurnal mo* 
tion of tne sun, by a person sailing in a boat ? 

510. In what part of the ellipse described by a planet, 
is the sun placed ? 

511. When do the highest and lowest tides happen ? 
512 What is the reason that a synodical is longer than 

a periodical month ? 

518. How is the time determined, which the eartk 
takey to revolve around the sfln ? 

514. Why do you imagine the sun, moon, and planet* 
to be inhabited ? 



ELEMENTS OE ASTRONOMY. 207 

ol5. How do you prove that the planets revolve a- 
Fouad the sun, and not around the earth ? 

516. How is the time the sun is revolving on its axis 
determined ? 

517. What use is the horizontal parallax in astronom- 
ical calculations ? 

518. What is meant by the sun's apparent diameter ? 

519. How do eclipses of the moon prove the earth to 
be circular ? 

520. By whom were the spots on the sun's disc first 
discovered ? 

521. Is the parallax of a celestial body affected by* its 
distance ? 

522. How may eclipses for any particular year be 
readily calculated ? 

523. Explain the nature of eclipses by a diagram, 

524. Are tides generated in lakes ? 

525. How do you prove that the motion of the earth 
round the sun. is from west to east ? 

526. How do you prove that light is progressive in its 
motion ? 

527. How long would a cannon ball be in going to the 
nearest fixed star, if it were to continue with the same 
velocity as when first projected ? 

528. How may we know when to expect a solar or 
lunar eclipse ? 

529. Illustrate the nature of parallax. 

530. Illustrate the causes of the opposition and con* 
junction of the superior planets. 

531. Illustrate the causes of the inferior and superior 
conjunctions of the inferior planets. 

532. What kind of appearance does the earth present 
to the moon ? 

53S. How do you determine the distances of the supe- 
rior planets, exclusively by their parallax ? 

534. How are lunar eclipses useful in determining the 
longitudes of places ? 

53.1. Illustrate the retrograde motion of the superior 
planets. 

556. How were eclipses formerly beheld ? 

537. How do you determine the distances of the plan- 
ets from the earth or sun ? 



£08 QUESTIONS UPON TfHE 

538. Explain the nature of the places of the sun and 
earth ; and show me by a diagram, liow you would de- 
termine the earth's place in the ecliptic at any time. 

559. It is not possible for Mercury to transit the sun, 
excepting on two days in the year : which are they ? 

540. What is the sun's apparent diameter in Decem- 
ber, and what is it in June ? 

541. How do navigators prove the earth to he round ? 

542. What other proof have we that Mercury's orbit 
Is within the orbit of the earth, besides her never being 
visible in the night ? 

543. Is the angle any body forms at the eye of a spec- 
tator, proportioned to its distance ? 

544. What means have effectually determined the 
magnitude of the earth ; and by whom were they em- 
ployed ? 

545. What particular advantages have resulted from 
the observations of transits ? 

546. Why do astronomers consider the sun to be a 
iolid body ? 

547. What proof can you adduce, that the orbit of the 
earth is elliptical, and not perfectly circular ? 

548. How do you account for the sun's rays causing 
heat in substances ? 

549. How do mathematicians determine the altitudes 
of the clouds ? 

550. How is the magnitude of the moon ascertained ? 

551. What is the reason that comets are not terrible 
to us, as they were to the ancients ? 

55%. What is meant by the moon's latitude, and how 
great must her latitude be when near her nodes, not to 
foe eclipsed ? 

553. Is the sun deprived of his light during an eclipse: 
if not, how do you account for his appearing so ? 

554. Explain by a diagram,the nature of the solar and 
lunar ecliptic limit. 

555. How are the days in a northern and southern lat- 
itude proportioned with regard to each other ? 

556. Why is the internal part of the earth considered 
to be filled with metals ? 

557. What is the reason that as the sun is nearer to 
us in winter than it is in the summer, it is colder in the 
former than in the latter season ? 



ELEMENTS OK ASTRONOMY. £09 

558. How do you explain by a person riding in a 
boat, the apparent motion of the sun ? 

559. How do you prove that it is in consequence of 
the inclination of the axis of the earth, the day and night 
is unequally divided ? 

560. By what are the inequalities of the earth's 
surface occasioned ? 

561. How high do the vapours ascend, which arise 
from the earth J 

56*2. Of what is the internal part of the earth composed. 2 

563. How was it that the satellites of Jupiter were 
first discovered ? 

564. At a new moon,what kinds of appearances do the 
earth and sun present to the inhabitants of the moon ? 

565. Explain the nature of determining the difference 
of longitude of any two places, by the eclipses of the 
satellites of Jupiter. 

566. How long would sound be travelling from the 
earth to the nearest fixed star ? 

567. When the moon appears eclipsed to us, what 
body appears eclipsed to the moon ? 

568. How do modern astronomers distinguish the dif- 
ferent stars in the constellations ? 

569. What proof have we that the darkness which 
happened at the time of our Saviour's crucifixion, was 
not a solar eclipse ? 

570. How do you find the distance of any inferior 
planet from the sun ? 

571. Explain the nature of a planet's elongation ? 

572. Illustrate the retrograde motion of an inferior 
planet ? 

573. How would you at first sight tell me the name of 
any planet you observed ? 

57b. What is the exact time the moon's nodes take to 
revolve around the ecliptic ? 

575. What advantage did Columbus derive from the 
superstitions of the West Indians, respecting eclipses ? 

576. Which is the readiest way to find the name of 
any particular star we observe in the heavens ? 

517* How do the Mexicans act during eclipses ? 



18* 



210 ■6CESTIOKS UPON THE 



PART III. 



PROMISCUOUS EXAMPLES, 

ON THE 

PLANETARY PROBLEMS. 



578. If the geocentric place of Jupiter, December 
10th; 1822, be I s 29° 26', and that of Saturn on the 
same day I s 5° 48', what is the difference in the times of 
their culminating? 

579. December 18th 1823, does Saturn rise before or 
after the sun '? 

580. The difference of longitude of two places is 117° 
18 N ; what is their difference in time ? 

581. The diurnal arc of Saturn is 173° 11' on a certain 
day ; what hour does the sun rise ? 

582. Being at sea, when the sun was on the meridian, 
I found, by a well regulated time-piece, that it was l h 
19' 60" P.M. at New- York ; in what longitude was I ? 

583. What is the heliocentric longitude of Jupiter, 
August 4th 1824? 

584. Is Venus a morning or evening star August 4th 
1825 ? 

585. What is the geocentric longitude of Jupiter, 
May 4th 1828 ? 

586. On what day will Jupiter enter y in the year 
1823 ? 

587. The moon was eclipsed August 3d 1822 t the be- 
ginning of this eclipse at London was August 2d 10 h 52' 
P.M. : what time did it begin at Paris, Madrid, and 
Petersburgh ? 



BLEMENtS 0E JLgTRONOMY. 211 

588. When the sun's diurnal arc is 200°, at what hour 
iocs he rise and set ? 

589. When it is 3 h A.M. at London, what is the time 
at Washington ? 

590. When in the year 1823 will Mars appear on the 
meridian at midnight ? 

591. How many days elapse between two conjunc- 
tions of Saturn and Venus ? 

592. On September 11th at London the sun sets at 
5 h 33'; what is the length of his nocturnal arc ? 

593* If Venus begin to be a morning star, March 10th 
1823 ; when will she next begin to be an evening star ? 

594 Will Jupiter be a morning or an evening star 
September 6th 1824 ? 

595. On what day will Saturn next enter $1 ? 

596. What is the longitude of the earth June 8th 1823? 
59T. How many days elapse between two conjunctions 

of Jupiter and Venus ? 

598. How far is the sun distant from the meridian of 
*ny place at llj h A. M. ? 

599. When Mars rises at 6 o'clock A.IVL how many 
hours is he above the horizon ? 

600. When the sun continues above the horizon ll h 
19', what hour does he rise and set, and what is the 
length of his diurnal arc ? 

601. Does Jupiter rise before or after the sun No- 
vember 17th 1824 ? 

602. Two stars are observed to be on the meridian of 
a certain place within 2f h of each other, what is their 
difference of longitude ? 

60S. What is the longitude of that place, on the me- 
ridian of which the sun appears 2| h before he appears on 
the meridian of London i 

604 The geocentric longitude of Jupiter on June 6th 
1822 was I s 20° 29', and of the sun 2 s 13° 13', how long 
did he rise before the sun, he being a morning star ? 

605. What is the difference in the longitudes of 
the Earth and Saturn, April 8th 1825. 

606. When will Venus have no heliocentric longi- 
tude in the year 1825 ? 



212 QUESTIONS UPON THE 

607. What is the geocentric place of Mars, Novem- 
ber 6th 1826? 

608. When in the year 1824 will the earth and Venus 
have a sextile aspect ? 

609. WiH Venus transit the sun in the year 1823 ? 

610. When will Jupiter next pa<s his descending node? 
611 In what sign of the zodiac will Herschell be 

August 19th 1824 ? 

612. If Venus be observed to set lj h after the sun, 
what is her elongation ? 

613. What is the sun's place November 6th 1825 ? 

614. When in the year 1825, will Venus and Mars be 
In conjunction ? 

615. October 19th 1822, Mars rose at B h 28' A.M., 
and the sun 6 h 48'; what was their difference of longitude? 

616. How many days elapse between two conjunctions 
$f the earth and Mercury ? 

6 IT. When in the year 1823 will Jupiter be on the me- 
ridian at midnight ? 

618. When will Mars and Saturn appear next on the 
meridian together ? 

619. Will the earth appear to transit the sun to the 
inhabitants of Jupiter in the year 1823 ? 

620- What will be the geocentric place of Saturn May 
4th 1823 ? 

621. When will Saturn and Herschell next have a 
A aspect? 

622. When Saturn continues above the horizon 17 h , 
at what hour does the sun rise and set, and what is the 
length of his diurnal arc ? 

623. If Jupiter begin to be a morning star May 4th 
1822, when will he begin to be a morning star again ? 

624. How many days from January 1st 1824, before 
Venus and the earth will be in conjunction ? 

625 When next will Saturn and Jupiter appear on the 
meridian 4 h after each other ? 

626. What will be the geocentric place of Venus Ju- 
ly 8th 1823 ? 

627. Will Venus appear to transit the sun in the year 
1824 ? 

628. On what day will the next conjunction of Saturn 
and Herschell be ? 



ELEMENTS OE ASTRONOMY. 21S 

629. When in the year 1824, will Venus and Jupiter 
be in heliocentric conjunction ? 

630. What is the longitude of the moon April 4th 
1824? 

631. What is the place of Mercury as seen from the 
sun on July 7th 1825 ? 

652. What will be the longitude of the moon Novem- 
ber 7 th 1823, and will she be to the east or to west of 
the sun ? 



214 QUESTIONS ¥PON THE 

PART IV. 



PROMISCUOUS QUESTIONS 

TO BE ANSWERED BY THE GLOBES: 



633. What is a vertical circle ? 

634. How many zones are there? 

635. How are the parallels of latitude drawn on the 
celestial globe ? 

656. What place is that whose latitude is 48° 23' N. 
and longitude 4° 29' W. ? 

637. What are the declinations and right ascension* 
of Cantor and Pollux ? 

638 At Palermo June 17ih r 9 h 18' A /M what are 
the sun's azimuth and altitude ? 

639. What is the right ascension of Saturn August 
17th 1824? 

640. In an unknown latitude I observed the alti- 
tude of Aldebaran to be 29° 18', and his azimuth S. 28* 
E; this was at9 h 16' P.M. on what day was this, and 
in what latitude was I ? 

641. How far distant is Procyon from the northern 
Pole Htar ? 

642. When it is 9 o'clock AM. at Lyons, May 8th 
where is the sun in the zenith, to what places is it 
midnight, where is he rising, and where setting ? 

643. On what day will the inhabitants of North 
Cape begin to behold the luminary of day after their 
long and tedious winter night ? 

644. What are the Antoeci of Philadelphia ? 

645. How is the wooden horizon of an artifical globe 
generally divided ? 

646. What are the latitudes and longitudes of Pres- 
fourg, Canton, and Aleppo ? 

647. What is the length of the day at Mecca when 
the sun rises at 4 h 19' at London ? 



ELEMENTS OB ASTRONOMY. 215 

648. How far south of Paris is that place where the 
fun is vertical on December 11th ? 

649. What will he the difference in the right as- 
censions of Saturn and Herschell, May ISth 1825 ? 

650. What are the latitude and longitude of Lyrse ? 

651. At what hour will the light invigorate the 
korizon of London, on October 19th ? 

652. What is the difference of the lengths of the 
longest day at Buda and Ispahan ? 

653. What are the azimuth and altitude of Sirius 
at Nova Zembla, September 6th 8i h P.M. ? 

654. Will Jupiter be above the horizon of Phila- 
delphia, September 18th 1823 at9 h P.M. 

655. At 7 h A. M* at London April 4th where is 
the sun vertical, to what places is he rising, and to 
what places is be setting ? 

656. What stars are on the meridian at Madrid 
when it is TJ h P.M. at London, February 8th ? 

65T. On what day is the right ascension of the sun 117°? 

658. To what places on the earth is the day of the 
same length as at Paris ? 

659. What d oes the celestial globe represent ? 

660. To what places on the earth does the sun ap« 
pear south the same time he does at Moscow ? 

661. How far is Whitehaven north of Guiana? 
66^. Is the sun ever vertical to the inhabitants of 

Port Royal ; if so, on what days ? 

663. What is the right ascension of Venus April 
18th 1823? 

664. In what manner does the celestial globe repre- 
sent the apparent motion of the stars, Sec. ? 

665. What part of the earth does the torrid zone 
comprehend ? 

666. How many degrees colder is it at Petersburgh 
than at London ? 

66T. What is the terrestrial globe ? 

668. What are the rising and setting amplitudes of 
the sun at Lima, November 4th, and at what hour 
does he rise and set ? 

669. In what sign will Mars be wheu his right as- 
cension is 246° ? 



£16 QUESTIONS UPON ASTRONOMY. 

670. At what hour does Sirius rise at Bristol,Novemf 
her 4th ? 

671. What stars are on the meridian of Syracuse at 
midnight, November 15th ? 

672. What is the greatest rising amplitude the sun 
has at London ? 

673. On November 25th 1822, the longitude of Venus 
was 270° 8' ; was she a morning or an evening star, 
and at what hour did she rise and set ? 

674. How long does constant day continue at Nortli 
West Cape, Nova Zembla ? 

675. What place is that whose latitude is 53° M 
It. and longitude 3° 12' W. ? 

676. How far distant is Jerusalem from Naples ? 

677. How far east of Cork is Paris ? 

678. What is the brazen meridian of the terrestri- 
al globe? Jl+** *,,,j 

679. If an eclipse of the moon begin at 7*> 19 U" 
at London, what time will it commence at Falmouth ? 

680. How are the constellations represented on the 
celestial globe ? , 

681. What is the longitude of a celestial body ? 

682. What are the poles of the horizon ? 

683. On June 26th U§ h P.M. 1824, the moon will be 
eclipsed where on the earth will it be visible ? 

684. Will the Sun or Mars have the greater right as- 
eension November 7th ,1823 ? 

685. How is the zodiac represented on the celestial 
globe ? . 

686. At North West Cape when does constant day 
begin, and how long does it continue ? 

687. Will Jupiter be a morning or an evening star 
September 19th 1825? , 

688. I observed the Pleiades to culminate at 9 16 
when their altitude was 47° 19' ; what were the latitude 
and day of the month ? 

689. What part of the earth does the north temperate 
ssone include ? 



the end. 



